CN206498412U - A kind of five rank hyperchaotic systems of wide parameter region - Google Patents
A kind of five rank hyperchaotic systems of wide parameter region Download PDFInfo
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Abstract
The utility model provides a kind of five rank hyperchaotic systems of wide parameter region, for exporting five road chaotic signals, including the first via to the 5th road circuit, the first via circuit includes the first inverting integrator and the first phase inverter, second road circuit includes sign function signal generator, second inverting integrator and the second phase inverter, the 3rd road circuit includes the 3rd inverting integrator and the 3rd phase inverter, the 4th road circuit includes SIN function signal generator, hyperbolic sine function signal generator, 4th inverting integrator and the 4th phase inverter, the 5th road circuit includes the 5th inverting integrator and the 5th phase inverter.The utility model hyperchaotic system can just realize the design of circuit module by the basic electronic component such as simple calculations amplifier, resistance, electric capacity, circuit structure design is simple, it is easy to adjust, hyperchaos characteristic can be presented in larger parameter area, and there are typical Hyperchaotic Attractors.
Description
Technical field
The utility model is related to a kind of chaos system, and in particular to hyperchaos characteristic can be presented in one kind in wide parameter area
Five rank hyperchaotic systems.
Background technology
Chaology in the past few decades in have a great development.Chaos system is due to its complicated power scholarship and moral conduct
To be had a wide range of applications in fields such as biosystem, electronic engineering, computer and signal transactings.Rssler in 1979 is first
Hyperchaos phenomenon is described, henceforth, the other hyperchaotic systems of many scholar's research.Compared with common chaos system
Compared with when applying in Practical Project, hyperchaotic system turns into prioritizing selection because of its complicated dynamic structure.In recent years, in order to
More valuable chaos system is obtained in actual applications, and how more research centers of gravity produces with complex topology knot if being concentrated on
The chaos attractor of structure.At present, hyperchaos can only be presented or even mixed in most of chaos system in narrower parameter area
Ignorant characteristic, the utility model proposes five rank hyperchaotic systems hyperchaos characteristic can then be presented in very wide parameter area.
In addition, the circuit realiration of many chaos systems is not completely the same with system in engineering, do not reach preferable state, there is many
Error and interference, therefore with larger room for improvement.
Utility model content
The purpose of this utility model is a kind of five ranks hyperchaotic system of offer, and the five ranks hyperchaotic system circuit structure is clear
It is clear, realize simple, and be presented that the systematic parameter scope of hyperchaos characteristic is larger, so as to obtain the chaotic signal of complexity.
Therefore, the utility model is adopted the following technical scheme that：
Five rank hyperchaotic systems of a kind of wide parameter region, for exporting five road chaotic signals, including the first via to the 5th
Road circuit, the first via circuit includes the first inverting integrator and the first phase inverter, and second road circuit includes symbol letter
Number signal generators, the second inverting integrator and the second phase inverter, the 3rd road circuit include the 3rd inverting integrator and the
Three phase inverters, the 4th road circuit includes SIN function signal generator, hyperbolic sine function signal generator, the 4th anti-phase
Integrator and the 4th phase inverter, the 5th road circuit include the 5th inverting integrator and the 5th phase inverter；Wherein：
First inverting integrator has four inputs and an output end, and its four inputs are respectively used to letter
Number-x ,-y ,-z and w input, the output signal of output end is x；The input signal of first phase inverter is x, output signal
For-x；
Second inverting integrator has four inputs and an output end, and its four inputs are respectively used to letter
Number-x ,-y, the input of-z and sign function signal generator output signal, the output signal of output end is y；Described second is anti-phase
The input signal of device is that y, output signal are-y, and the input signal of the sign function signal generator is y；
3rd inverting integrator has two inputs and an output end, and two input is respectively used to signal
X and y input, the output signal of output end is z；The input signal of 3rd phase inverter be z, output signal be-z；
4th inverting integrator has three inputs and an output end, and its three inputs are respectively used to letter
Number-x ,-sin and-sinh input, the output signal of output end is w；The input signal of 4th phase inverter is w, output signal
For-w；The input signal of the SIN function signal generator is that-u, output signal are-sin；The hyperbolic sine function signal
Generator has two inputs and an output end, and two input is respectively used to signal-w and w input, output end
Output signal is-sinh；
The input signal of 5th inverting integrator is that-w, output signal are u；The input signal of 5th phase inverter
It is-u for u, output signal；
The input and the 3rd inverting integrator that the output end of first inverting integrator connects the first phase inverter respectively are used
In input signal x input；The output end of first phase inverter connects the first inverting integrator, the second inverting integrator respectively
It is used for input signal-x input with the 4th inverting integrator；
The output of the sign function signal generator terminates the second inverting integrator and sent out for incoming symbol function signal
The input of raw device output signal, the output end of the second inverting integrator connects the input of the second phase inverter, sign function respectively
The input of signal generator and the 3rd inverting integrator are used for input signal y input；The output end of second phase inverter point
Not connecing the first inverting integrator and the second inverting integrator is used for input signal-y input；
The input of output the 3rd phase inverter of termination of 3rd inverting integrator；The output end difference of 3rd phase inverter
Connecing the first inverting integrator and the second inverting integrator is used for input signal-z input；
The output end of 4th inverting integrator connects hyperbolic sine function signal generator and the first anti-phase integration respectively
Device is used for input signal w input and the input of the 4th phase inverter；The output end of 4th phase inverter connects double respectively
Bent SIN function signal generator is used for input signal-w input and the input of the 5th inverting integrator；Hyperbolic sine letter
Output the 4th inverting integrator of termination of number signal generator is used for input signal-sinh input；SIN function signal is sent out
Output the 4th inverting integrator of termination of raw device is used for input signal-sin input；
The input of output the 5th phase inverter of termination of 5th inverting integrator, the output end of the 5th phase inverter
Connect the input of SIN function signal generator.
Further, first inverting integrator includes the first operational amplifier（U1）, the first electric capacity（C1）, the 11st
Resistance（R11）, the 12nd resistance（R12）, the 13rd resistance（R13）With the 14th resistance（R14）；First operational amplifier
（U1）In-phase input end ground connection, inverting input connects the 11st resistance respectively（R11）, the 12nd resistance（R12）, the 13rd
Resistance（R13）With the 14th resistance（R14）One end, the first electric capacity is connected between inverting input and output end（C1）；It is described
11st resistance（R11）, the 12nd resistance（R12）, the 13rd resistance（R13）With the 14th resistance（R14）The other end difference
Constituting the first inverting integrator is used for input signal-x ,-y ,-z and w four inputs, first operational amplifier（U1）
Output end constitute the first inverting integrator output end.
Further, second inverting integrator is identical with the structure of the first inverting integrator.
Further, the 3rd inverting integrator includes the 5th operational amplifier（U5）, the 3rd electric capacity（C3）, the 20th
One resistance（R21）With the 22nd resistance（R22）；5th operational amplifier（U5）In-phase input end ground connection, it is anti-phase defeated
Enter end and connect the 21st resistance respectively（R21）With the 22nd resistance（R22）One end, between inverting input and output end
Connect the 3rd electric capacity（C3）；21st resistance（R21）With the 22nd resistance（R22）The other end respectively constitute the 3rd
Inverting integrator is used for input signal x and y two inputs, the 5th operational amplifier（U5）Output end constitute the 3rd
The output end of inverting integrator.
Further, the 4th inverting integrator includes the 7th operational amplifier（U7）, the 4th electric capacity（C4）, the 20th
Three resistance（R23）, the 24th resistance（R24）With the 25th resistance（R25）；7th operational amplifier（U7）Same phase
Input end grounding, inverting input connects the 23rd resistance respectively（R23）, the 24th resistance（R24）With the 25th electricity
Resistance（R25）One end, between inverting input and output end connect the 4th electric capacity（C4）；23rd resistance（R23）,
24 resistance（R24）With the 25th resistance（R25）The other end respectively constitute the 4th inverting integrator be used for input signal-
X ,-sin and-sinh three inputs, the 7th operational amplifier（U7）Output end constitute the 4th inverting integrator
Output end.
Further, the 5th inverting integrator includes the 9th operational amplifier（U9）, the 5th electric capacity（C5）With the 6th
16 resistance（R66）；9th operational amplifier（U9）In-phase input end ground connection, inverting input connection the 66th electricity
Resistance（R66）One end, between inverting input and output end connect the 5th electric capacity（C5）；66th resistance（R66）'s
The other end constitutes the input of the 5th inverting integrator, the 9th operational amplifier（U9）Output end constitute the 5th anti-phase product
Divide the output end of device.
Further, the sign function signal generator includes the 11st operational amplifier（U11）, the 12nd computing puts
Big device（U12）, the 19th resistance（R19）With the 20th resistance（R20）；11st operational amplifier（U11）It is same mutually defeated
Enter end ground connection, output end and connect the 19th resistance（R19）；12nd operational amplifier（U12）In-phase input end ground connection,
Inverting input connects the 19th resistance（R19）The other end, between inverting input and output end connect the 20th resistance
（R20）；11st operational amplifier（U11）Inverting input constitute the input of sign function signal generator, the
12 operational amplifiers（U12）Output end constitute sign function signal generator output end.
Further, the SIN function signal generator includes the 13rd operational amplifier（U13）To the 17th computing
Amplifier（U17）, the 26th resistance（R26）To the 39th resistance（R39）And the 5th diode（D5）To the 12nd pole
Pipe（D10）；And the 37th resistance（R37）, the 38th resistance（R38）With the 39th resistance（R39）For can power transformation
Resistance, wherein：
13rd operational amplifier（U13）In-phase input end ground connection, inverting input connect the 26th resistance
（R26）One end, between inverting input and output end connect the 27th resistance（R27）, the electricity of output end connection the 28th
Resistance（R28）One end；Tenth four-operational amplifier（U14）In-phase input end ground connection, inverting input connection the 20th
Eight resistance（R28）The other end, between inverting input and output end connect the 29th resistance（R29）, output end connection the
30 resistance（R30）；15th operational amplifier（U15）In-phase input end ground connection, inverting input connection the 30th
Resistance（R30）The other end and the 34th resistance（R34）One end, between inverting input and output end connect the 31st
Resistance（R31）, output end the 35th resistance of connection（R35）One end；16th operational amplifier（U16）It is same mutually defeated
Enter end ground connection, inverting input connects the 32nd resistance（R32）One end, between inverting input and output end connect the 3rd
13 resistance（R33）, output end the 34th resistance of connection（R34）The other end；
17th operational amplifier（U17）In-phase input end connect the 35th resistance respectively（R35）It is another
End, the 9th diode（D9）Negative pole and the tenth diode（D10）Positive pole, inverting input connect the 36th resistance
（R36）One end, the 39th resistance（R39）One end and the 5th diode（D5）Negative pole, the 6th diode（D6）Just
Pole, output end connects the 37th resistance（R37）One end, the 39th resistance（R39）The other end, the 7th diode（D7）
Negative pole and the 8th diode（D8）Positive pole；37th resistance（R37）Centre tap end connect the 9th diode（D9）
Positive pole and the tenth diode（D10）Negative pole；39th resistance（R39）Centre tap end connect the 5th diode（D5）
Positive pole, the 6th diode（D6）Negative pole, the 7th diode（D7）Positive pole and the 8th diode（D8）Negative pole；30th
Six resistance（R36）The other end connect the 38th resistance（R38）One end and its middle tap terminals；37th resistance
（R37）The other end and the 38th resistance（R38）Other end common ground；26th resistance（R26）It is another
End and the 32nd resistance（R32）The other end collectively form the input of SIN function signal generator, the 17th computing is put
Big device（U17）Output end constitute SIN function signal generator output end.
Further, the hyperbolic sine function signal generator includes the 18th operational amplifier（U18）To the 20th
Four-operational amplifier（U24）, the 40th resistance（R40）To the 65th resistance（R65）, the 6th electric capacity（C6）To the 9th electric capacity
（C9）, the first diode（D1）To the 4th diode（D4）And first triode（Q1）To the 4th triode（Q4）；Wherein：
18th operational amplifier（U18）In-phase input end connect the 42nd resistance（R42）With the 43rd
Resistance（R43）One end, inverting input connect the 40th resistance（R40）One end, connect between inverting input and output end
Connect the 41st resistance（R41）, output end the first diode of connection（D1）Negative pole and the second diode（D2）Positive pole；It is described
40th resistance（R40）With the 43rd resistance（R43）The other end ground connection；19th operational amplifier（U19）It is same
Phase input connects the 47th resistance（R47）One end, inverting input connect the first triode（Q1）With the second triode
（Q2）Emitter stage, between inverting input and output end connect the 46th resistance（R46）, the electricity of output end connection the 48th
Resistance（R48）One end；47th resistance（R47）The other end ground connection；First triode（Q1）Colelctor electrode connection the 6th electricity
Hold（C6）With the 44th resistance（R44）One end, the first triode（Q1）Base stage connect the 6th electric capacity（C6）The other end,
44th resistance（R44）The other end and the first diode（D1）Positive pole；Second triode（Q2）Colelctor electrode connection the
Seven electric capacity（C7）With the 45th resistance（R45）One end, the second triode（Q2）Base stage connect the 7th electric capacity（C7）It is another
One end, the 45th resistance（R45）The other end and the second diode（D2）Negative pole；20th operational amplifier
（U20）In-phase input end connect the 50th resistance（R50）One end, inverting input connect the 48th resistance（R48）'s
The other end, connects the 49th resistance between inverting input and output end（R49）, output end the 51st resistance of connection
（R51）One end, the 50th resistance（R50）The other end ground connection；21st operational amplifier（U21）Homophase input
The 56th resistance of end connection（R56）With the 58th resistance（R58）One end, inverting input connect the 55th resistance
（R55）One end, between inverting input and output end connect the 57th resistance（R57）, output end the 3rd diode of connection
（D3）Negative pole and the 4th diode（D4）Positive pole；58th resistance（R58）With the 55th resistance（R55）The other end
Ground connection；22nd operational amplifier（U22）In-phase input end connect the 62nd resistance（R62）One end, it is anti-phase
Input connects the 3rd triode（Q3）With the 4th triode（Q4）Emitter stage, is connected between inverting input and output end
61 resistance（R61）, output end the 63rd resistance of connection（R63）；62nd resistance（R62）Other end ground connection, the
Three triodes（Q3）Colelctor electrode connect the 8th electric capacity（C8）With the 59th resistance（R59）One end, the 3rd triode（Q3）
Base stage connect the 8th electric capacity（C8）The other end, the 59th resistance（R59）The other end and the 3rd diode（D3）Just
Pole；4th triode（Q4）Colelctor electrode connect the 9th electric capacity（C9）With the 60th resistance（R60）One end, the 4th triode
（Q4）Base stage connect the 9th electric capacity（C9）The other end, the 60th resistance（R60）The other end and the 4th diode（D4）'s
Negative pole；23rd operational amplifier（U23）In-phase input end connect the 65th resistance（R65）One end, it is anti-phase
Input connects the 63rd resistance（R63）The other end, between inverting input and output end connect the 64th resistance
（R64）, output end the 52nd resistance of connection（R52）One end, the 65th resistance（R65）The other end ground connection；Described
20 four-operational amplifiers（U24）In-phase input end connect the 54th resistance（R54）One end and the 52nd resistance
（R52）The other end, inverting input connect the 51st resistance（R51）The other end, between inverting input and output end
Connect the 53rd resistance（R53）, the 54th resistance（R54）The other end ground connection；
42nd resistance（R42）With the 56th resistance（R56）The other end respectively constitute hyperbolic sine function
Signal generator is used for input signal-w and w two inputs, the 20th four-operational amplifier（U24）Output end constitute it is double
The output end of bent SIN function signal generator.
In the rank hyperchaotic system equation of the utility model five containing three common nonlinear functions, i.e. sign function, just
String function and hyperbolic sine function.Wherein, it is different from traditional self-oscillation and produces SIN function, the utility model passes through waveform
The mode of conversion completes triangular wave to the conversion of sine wave, realizes that the input of the waveform external world is controllable.The wherein reality of hyperbolic sine function
Existing process, circuit different from the past according to the output characteristic curve of diode, generally use the equivalent model of diode, and
It is the definition according to hyperbolic sine function, the specific requirement of hyperbolic sine function is realized, so as to reduce
Signal errors.
Physical circuit principle of the present utility model is as follows：
In first via circuit, using the first inverting integrator output signal x, the first inverter output signal-x is utilized；The
In two road circuits, using the second inverting integrator output signal y, using the second inverter output signal-y, sign function is utilized
Signal generator output signal sign (y-0.5)；In 3rd road circuit, using the 3rd inverting integrator output signal z, is utilized
Three inverter output signal-z；It is defeated using the 4th phase inverter using the 4th inverting integrator output signal w in 4th road circuit
Go out signal-w, using SIN function signal generator output signal-sin (u), exported using hyperbolic sine function signal generator
Signal-sinh (w+1)；In 5th road circuit, using the 5th inverting integrator output signal u, exported and believed using the 5th phase inverter
Number-u.
Kinetic model corresponding to the rank hyperchaotic system of the utility model five is：
（1）
Wherein, the nonlinear function in formula is respectively：
（2）
In formula, x, y, z, w, u are the output signal value of the rank hyperchaotic system of the utility model five respectively, are become herein for state
Amount；A, b, c, d, e are systematic parameter, take real number.The dominant dynamic characteristic of system can be carried out by Lyapunov spectrograms
Analysis.In chaos is interval, one group of parameter is arbitrarily chosen, when parameter a, b, c, d take fixed value and a=10, b=0.03, c=150,
D=0.8, and during e changes, Lyapunov spectrograms as shown in Figure 9 can be obtained.As seen from Figure 9, system exist two with
The upper Lyapunov indexes more than 0（L1, L2 and L3）, illustrate that the rank hyperchaotic system of the utility model five can be in wider ginseng
Hyperchaos characteristic, or even super hyperchaos characteristic are presented in number scope, the system of further relating to has considerably complicated dynamics,
It is adapted to apply in secret communication.
To sum up, the beneficial effects of the utility model are：
1. containing three common nonlinearity functions in five rank hyperchaotic systems of the utility model construction, system equation, respectively
The realization of nonlinear function hardware circuit only needs the devices such as common operational amplifier, resistance, electric capacity, diode, with low cost,
Realize simply, it is easy to operate；
2. five rank hyperchaotic systems of the utility model construction, can be presented hyperchaos characteristic in very wide parameter area,
Or even super hyperchaos characteristic；
3. the five rank hyperchaotic systems that the utility model is built, by carrying out the Multisim circuit simulations of chaotic model,
The chaos attractor phasor of system can be observed on oscillograph.
Brief description of the drawings
Fig. 1 is the circuit structure theory diagram of the rank hyperchaotic system of the utility model five；
Fig. 2 is the electrical block diagram of the utility model first via circuit；
Fig. 3 is the electrical block diagram of the second road of the utility model circuit；
Fig. 4 is the electrical block diagram of the road circuit of the utility model the 3rd；
Fig. 5 is the electrical block diagram of the inverting integrator of the utility model the 4th and the 4th phase inverter；
Fig. 6 is the electrical block diagram of the road circuit of the utility model the 5th；
Fig. 7 is the electrical block diagram of the utility model SIN function signal generator；
Fig. 8 is the electrical block diagram of the utility model hyperbolic sine function signal generator；
Fig. 9 is the Lyapunov spectrograms that the rank hyperchaotic system of the utility model five changes with parameter e；
Figure 10 is the circuit simulation x-y phasors of the rank hyperchaotic system of the utility model five；
Figure 11 is the circuit simulation y-z phasors of the rank hyperchaotic system of the utility model five；
Figure 12 is the circuit simulation x-w phasors of the rank hyperchaotic system of the utility model five；
Figure 13 is the circuit simulation z-w phasors of the rank hyperchaotic system of the utility model five.
Embodiment
Below by specific embodiment to the utility model proposes five rank hyperchaotic systems design principle carry out it is detailed
Description.
A kind of five rank hyperchaotic systems of wide parameter region as shown in Figure 1, for exporting five road chaotic signals, including the
All the way to the 5th road circuit, and the first via circuit includes the first inverting integrator and the first phase inverter, the second road electricity
Road includes sign function signal generator, the second inverting integrator and the second phase inverter, and it is anti-that the 3rd road circuit includes the 3rd
Phase integral device and the 3rd phase inverter, the 4th road circuit include SIN function signal generator, hyperbolic sine function signal and sent out
Raw device, the 4th inverting integrator and the 4th phase inverter, the 5th road circuit include the 5th inverting integrator and the 5th phase inverter；
Wherein：
First inverting integrator has four inputs and an output end, and its four inputs are respectively used to letter
Number-x ,-y ,-z and w input, the output signal of output end is x；The input signal of first phase inverter is x, output signal
For-x；
Second inverting integrator has four inputs and an output end, and its four inputs are respectively used to letter
Number-x ,-y, the input of-z and sign function signal generator output signal, the output signal of output end is y；Described second is anti-phase
The input signal of device is that y, output signal are-y, and the input signal of the sign function signal generator is y；
3rd inverting integrator has two inputs and an output end, and two input is respectively used to signal
X and y input, the output signal of output end is z；The input signal of 3rd phase inverter be z, output signal be-z；
4th inverting integrator has three inputs and an output end, and its three inputs are respectively used to letter
Number-x ,-sin and-sinh input, the output signal of output end is w；The input signal of 4th phase inverter is w, output signal
For-w；The input signal of the SIN function signal generator is that-u, output signal are-sin；The hyperbolic sine function signal
Generator has two inputs and an output end, and two input is respectively used to signal-w and w input, output end
Output signal is-sinh；
The input signal of 5th inverting integrator is that-w, output signal are u；The input signal of 5th phase inverter
It is-u for u, output signal；
The input and the 3rd inverting integrator that the output end of first inverting integrator connects the first phase inverter respectively are used
In input signal x input；The output end of first phase inverter connects the first inverting integrator, the second inverting integrator and respectively
Four inverting integrators are used for input signal-x input；
The output of the sign function signal generator terminates the second inverting integrator and sent out for incoming symbol function signal
The input of raw device output signal, the output end of the second inverting integrator connects the input of the second phase inverter, sign function respectively
The input of signal generator and the 3rd inverting integrator are used for input signal y input；The output end of second phase inverter point
Not connecing the first inverting integrator and the second inverting integrator is used for input signal-y input；
The input of output the 3rd phase inverter of termination of 3rd inverting integrator；The output end difference of 3rd phase inverter
Connecing the first inverting integrator and the second inverting integrator is used for input signal-z input；
The output end of 4th inverting integrator connects hyperbolic sine function signal generator and the first anti-phase integration respectively
Device is used for input signal w input and the input of the 4th phase inverter；The output end of 4th phase inverter is connecing hyperbolic just respectively
String function signal generator is used for input signal-w input and the input of the 5th inverting integrator；Hyperbolic sine function is believed
Output the 4th inverting integrator of termination of number generator is used for input signal-sinh input；SIN function signal generator
Output termination the 4th inverting integrator be used for input signal-sin input；
The input of output the 5th phase inverter of termination of 5th inverting integrator, the output termination of the 5th phase inverter is just
The input of string function signal generator.
In terms of the realization of circuit concrete structure：
As shown in Fig. 2 first inverting integrator includes the first operational amplifier U1, the first electric capacity C1, the 11st electricity
Hinder R11, the 12nd resistance R12, the 13rd resistance R13 and the 14th resistance R14；The first operational amplifier U1's is same mutually defeated
Enter end ground connection, inverting input connects the 11st resistance R11, the 12nd resistance R12, the 13rd resistance R13 and the 14th respectively
Resistance R14 one end, connects the first electric capacity C1 between inverting input and output end；The 11st resistance R11, the 12nd electricity
Resistance R12, the 13rd resistance R13 and the 14th resistance the R14 other end respectively constitute the first inverting integrator be used for input signal-
X ,-y ,-z and w four inputs, the output end of the first operational amplifier U1 constitute the output of the first inverting integrator
End.
As shown in figure 3, second inverting integrator is identical with the structure of the first inverting integrator, and the second anti-phase integration
Device includes the 3rd operational amplifier U3, the 15th resistance R15 to the 18th resistance R18 and the second electric capacity C2.
As shown in figure 4, the 3rd inverting integrator includes the 5th operational amplifier U5, the 3rd electric capacity C3, the 21st
Resistance R21 and the 22nd resistance R22；The in-phase input end ground connection of the 5th operational amplifier U5, inverting input difference
The 21st resistance R21 and the 22nd resistance R22 one end are connected, the 3rd electric capacity is connected between inverting input and output end
C3；The other end of the 21st resistance R21 and the 22nd resistance R22, which respectively constitutes the 3rd inverting integrator, to be used to input
Signal x and y two inputs, the output end of the 5th operational amplifier U5 constitute the output end of the 3rd inverting integrator.
As shown in figure 5, the 4th inverting integrator includes the 7th operational amplifier U7, the 4th electric capacity C4, the 23rd
Resistance R23, the 24th resistance R24 and the 25th resistance R25；The homophase input termination of the 7th operational amplifier U7
Ground, inverting input connects the 23rd resistance R23, the 24th resistance R24 and the 25th resistance R25 one end respectively,
The 4th electric capacity C4 is connected between inverting input and output end；The 23rd resistance R23, the 24th resistance R24 and
The 25 resistance R25 other end respectively constitute the 4th inverting integrator be used for three of input signal-x ,-sin and-sinh it is defeated
Enter end, the output end of the 7th operational amplifier U7 constitutes the output end of the 4th inverting integrator.
As shown in fig. 6, the 5th inverting integrator includes the 9th operational amplifier U9, the 5th electric capacity C5 and the 66th
Resistance R66；The in-phase input end ground connection of the 9th operational amplifier U9, inverting input connects the 66th resistance R66's
One end, connects the 5th electric capacity C5 between inverting input and output end；The other end of the 66th resistance R66 constitutes the 5th
The input of inverting integrator, the output end of the 9th operational amplifier U9 constitutes the output end of the 5th inverting integrator.
As shown in Fig. 2 first phase inverter includes the second operational amplifier U2, first resistor R1 and second resistance R2,
The second operational amplifier U2 in-phase input end ground connection, inverting input connection first resistor R1, inverting input with it is defeated
Go out connection second resistance R2 between end；The other end of the first resistor R1 constitutes the input of the first phase inverter, described second
Operational amplifier U2 output end constitutes the output end of the first phase inverter.
As seen in figures 3-6, the described second to the 5th phase inverter has and the first phase inverter identical structure.And described second
Phase inverter includes four-operational amplifier U4,3rd resistor R3 and the 4th resistance R4；3rd phase inverter includes the 6th computing
Amplifier U6, the 5th resistance R5 and the 6th resistance R6；4th phase inverter includes the 8th operational amplifier U8, the 7th resistance R7
With the 8th resistance R8；5th phase inverter includes the tenth operational amplifier U10, the 9th resistance R9 and the tenth resistance R10.
Put as shown in figure 3, the sign function signal generator includes the 11st operational amplifier U11, the 12nd computing
Big device U12, the 19th resistance R19 and the 20th resistance R20；The in-phase input end of the 11st operational amplifier U11 is through
One power supply V1 ground connection, output end connect the 19th resistance R19 one end；The homophase input of the 12nd operational amplifier U12
End ground connection, inverting input connects the 19th resistance R19 other end, and the 20th electricity is connected between inverting input and output end
Hinder R20；The inverting input of the 11st operational amplifier U11 constitutes the input of sign function signal generator, the tenth
Two operational amplifier U12 output end constitutes the output end of sign function signal generator.
As shown in fig. 7, the SIN function signal generator is put including the 13rd operational amplifier U13 to the 17th computing
Big device U17, the 26th resistance R26 to the 39th resistance R39 and the 5th diode D5 to the tenth diode D10；And institute
The 37th resistance R37, the 38th resistance R38 and the 39th resistance R39 are stated for variable resistor, wherein：
The in-phase input end ground connection of the 13rd operational amplifier U13, inverting input connects the 26th resistance R26
One end, the 27th resistance R27 is connected between inverting input and output end, output end connects the 28th resistance R28
One end；The in-phase input end ground connection of the tenth four-operational amplifier U14, inverting input connects the 28th resistance R28's
The other end, connects the 29th resistance R29 between inverting input and output end, output end connects the 30th resistance R30；It is described
15th operational amplifier U15 in-phase input end ground connection, inverting input connects the 30th resistance R30 other end and the 3rd
One end of 14 resistance R34s, connects the 31st resistance R31, output end connection the 30th between inverting input and output end
Five resistance R35 one end；The in-phase input end ground connection of the 16th operational amplifier U16, inverting input connection the 30th
Two resistance R32 one end, connects the 33rd resistance R33, output end connection the 34th between inverting input and output end
The other end of resistance R34；The in-phase input end of the 17th operational amplifier U17 connects the 35th resistance R35's respectively
The positive pole of the other end, the 9th diode D9 negative pole and the tenth diode D10, inverting input connects the 36th resistance R36
One end, the 39th resistance R39 one end and the 5th diode D5 negative pole, the 6th diode D6 positive pole, output end connects
Connect the 37th resistance R37 one end, the 39th resistance R39 other end, the 7th diode D7 negative pole and the eight or two pole
Pipe D8 positive pole；37th resistance R37 centre tap end connects the 9th diode D9 positive pole and the tenth diode D10
Negative pole；39th resistance R39 centre tap end connects the 5th diode D5 positive pole, the 6th diode D6 negative pole, the
Seven diode D7 positive pole and the 8th diode D8 negative pole；The 36th resistance R36 other end connects the 38th resistance
R38 one end and its middle tap terminals；The 37th resistance R37 other end and the 38th resistance R38 other end are common
Ground connection；The other end of the 26th resistance R26 and the 32nd resistance R32 other end collectively form SIN function signal
The input of generator, the 17th operational amplifier U17 output end constitutes the output end of SIN function signal generator.
As shown in figure 8, the hyperbolic sine function signal generator includes the 18th operational amplifier U18 to the 24th
Operational amplifier U24, the 40th resistance R40 to the 65th resistance R65, the 6th electric capacity C6 to the 9th electric capacity C9, the one or two pole
Pipe D1 to the 4th diode D4 and the first triode Q1 to the 4th triode Q4；Wherein：
The in-phase input end of the 18th operational amplifier U18 connects the 42nd resistance R42 and the 43rd resistance
R43 one end, inverting input connects the 40th resistance R40 one end, and the 40th is connected between inverting input and output end
One resistance R41, output end connects the first diode D1 negative pole and the second diode D2 positive pole；43rd resistance
R43 other end ground connection, the 40th resistance R40 other end is grounded through the 3rd power supply V3；The 19th operational amplifier U19
In-phase input end connect the 47th resistance R47 one end, inverting input connects the first triode Q1 and the second triode
Q2 emitter stage, connects the 46th resistance R46 between inverting input and output end, output end connects the 48th resistance
R48 one end；47th resistance R47 other end ground connection；First triode Q1 colelctor electrode connects the 6th electric capacity C6 and the
44 resistance R44 one end, the first triode Q1 base stage connects the 6th electric capacity the C6 other end, the 44th resistance R44
The other end and the first diode D1 positive pole；Second triode Q2 colelctor electrode connects the 7th electric capacity C7 and the 45th resistance
R45 one end, the second triode Q2 base stage connect the 7th electric capacity C7 other end, the 45th resistance R45 other end and
Second diode D2 negative pole；The in-phase input end of the 20th operational amplifier U20 connects the one of the 50th resistance R50
End, inverting input connects the 48th resistance R48 other end, and the 49th electricity is connected between inverting input and output end
R49 is hindered, output end connects the 51st resistance R51 one end；50th resistance R50 other end ground connection；Described 21st
Operational amplifier U21 in-phase input end connects the 56th resistance R56 and the 58th resistance R58 one end, anti-phase input
The 55th resistance R55 of end connection one end, connects the 57th resistance R57, output end between inverting input and output end
Connect the 3rd diode D3 negative pole and the 4th diode D4 positive pole；58th resistance R58 other end ground connection, the 50th
The five resistance R55 other end is grounded through second source V2；The in-phase input end connection the of the 22nd operational amplifier U22
62 resistance R62 one end, inverting input connects the 3rd triode Q3 and the 4th triode Q4 emitter stage, anti-phase input
The 61st resistance R61 is connected between end and output end, output end connects the 63rd resistance R63 one end；62nd electricity
R62 other end ground connection is hindered, the 3rd triode Q3 colelctor electrode connects the 8th electric capacity C8 and the 59th resistance R59 one end,
3rd triode Q3 base stage connects the 8th electric capacity C8 other end, the 59th resistance the R59 other end and the 3rd diode
D3 positive pole；4th triode Q4 colelctor electrode connects the 9th electric capacity C9 and the 60th resistance R60 one end, the 4th triode Q4
Base stage connect the 9th electric capacity C9 other end, the 60th resistance R60 other end and the 4th diode D4 negative pole；Described
23 operational amplifier U23 in-phase input end connects the 65th resistance R65 one end, inverting input connection the 60th
The three resistance R63 other end, connects the 64th resistance R64, output end connection the 50th between inverting input and output end
Two resistance R52 one end；65th resistance R65 other end ground connection；The 20th four-operational amplifier U24's is same mutually defeated
Enter the 54th resistance R54 of end connection one end and the 52nd resistance R52 other end, inverting input connection the 51st
The resistance R51 other end, connects the 53rd resistance R53 between inverting input and output end；54th resistance R54's is another
One end is grounded；The other end of the 42nd resistance R42 and the 56th resistance R56 respectively constitutes hyperbolic sine function signal
Generator is used for input signal-w and w two inputs, and the 20th four-operational amplifier U24 output end constitutes hyperbolic sine
The output end of function signal generator.
According to formula（1）The system dynamics model provided, makees variable scale compressed transform and time scale transformation to system,
Obtaining its state equation is：
（3）
When Selecting All Parameters a=10, b=0.03, c=150, d=0.8, e=15；C1=C2=C3=C4=C5=10nF is held in power taking, passes through
Numerical computations can be obtained：R11=R12=16.67k Ω, R13=R14=500 Ω, R15=R16=1.1k Ω, R17=33.3 Ω, R18=
The Ω of 66.7 Ω, R21=R22=5k Ω, R23=R24=6.25k Ω, R25=12.5k Ω, R66=333.3.
The value of other circuit elements is fixed value, and specific value is as follows：
The k of R1=R2=R3=R4=R5=R6=R7=R8=R9=R10=10k Ω, R19=13.5k Ω, R20=1.0
Ω, R26=1.0 k Ω, R27=R28=27 k Ω, R29=1.0 k Ω, R30=R31=R32=R33=R34=10k Ω, R35=
The k Ω of 4.70 k Ω, R36=5.6；R37 is variable resistor, and its parameter is：Maximum value 2.7 k Ω, Key=A, 30%；R38 is can
Become resistance, its parameter is：Maximum value 10 k Ω, Key=A, 50%；R39 is variable resistor, and its parameter is：The k of maximum value 10
Ω, Key=A, 50%；R40=R41=R42=R43=10 k Ω, R44=R45=100 k Ω, R46=R47=R48=R49=
10k Ω, R50=5 k Ω, R51=R52=20 k Ω, R53=R54=R55=R56=R57=R58=10 k Ω, R59=
The k Ω of R60=100 k Ω, R61=R62=R63=R64=10 k Ω, R65=5.
The model OPA743NA that first operational amplifier U1 is used to the 20th four-operational amplifier U24.
The model 2N1711 that first triode Q1 and the 3rd triode Q3 are used；Second triode Q2 and the four or three pole
The model 2N2904 that pipe Q4 is used.
The model D1N4148 that first diode D1 is used to the tenth diode D10.
Under the conditions of above-mentioned value, system can produce Hyperchaotic Attractors, and such as Figure 10-13 can be observed on oscillograph
Chaos attractor of the shown system in each phase plane.
Claims (9)
1. five rank hyperchaotic systems of a kind of wide parameter region, for exporting five road chaotic signals, it is characterised in that including first
The road circuits of Lu Zhi five, the first via circuit includes the first inverting integrator and the first phase inverter, the second road circuit bag
Sign function signal generator, the second inverting integrator and the second phase inverter are included, the 3rd road circuit includes the 3rd anti-phase product
Point device and the 3rd phase inverter, the 4th road circuit include SIN function signal generator, hyperbolic sine function signal generator,
4th inverting integrator and the 4th phase inverter, the 5th road circuit include the 5th inverting integrator and the 5th phase inverter；Wherein：
First inverting integrator have four inputs and an output end, its four inputs be respectively used to signal-x ,-
Y ,-z and w input, the output signal of output end is x；The input signal of first phase inverter be x, output signal be-x；
Second inverting integrator have four inputs and an output end, its four inputs be respectively used to signal-x ,-
Y ,-z and sign function signal generator output signal input, the output signal of output end is y；Second phase inverter it is defeated
It is that y, output signal are-y to enter signal, and the input signal of the sign function signal generator is y；
3rd inverting integrator has two inputs and an output end, and two input is respectively used to signal x and y
Input, the output signal of output end is z；The input signal of 3rd phase inverter be z, output signal be-z；
4th inverting integrator have three inputs and an output end, its three inputs be respectively used to signal-x ,-
Sin and-sinh input, the output signal of output end is w；The input signal of 4th phase inverter be w, output signal be-w；Institute
The input signal for stating SIN function signal generator is that-u, output signal are-sin；The hyperbolic sine function signal generator
With two inputs and an output end, two input is respectively used to signal-w and w input, the output letter of output end
Number be-sinh；
The input signal of 5th inverting integrator is that-w, output signal are u；The input signal of 5th phase inverter be u,
Output signal is-u；
The output end of first inverting integrator connects the input and the 3rd inverting integrator of the first phase inverter for defeated respectively
Enter signal x input；The output end of first phase inverter connects the first inverting integrator, the second inverting integrator and respectively
Four inverting integrators are used for input signal-x input；
The output of the sign function signal generator, which terminates the second inverting integrator, is used for incoming symbol function signal generator
The input of output signal, the output end of the second inverting integrator connects the input of the second phase inverter, sign function signal respectively
The input of generator and the 3rd inverting integrator are used for input signal y input；The output end of second phase inverter connects respectively
First inverting integrator and the second inverting integrator are used for input signal-y input；
The input of output the 3rd phase inverter of termination of 3rd inverting integrator；The output end of 3rd phase inverter connects respectively
One inverting integrator and the second inverting integrator are used for input signal-z input；
The output end of 4th inverting integrator connects hyperbolic sine function signal generator respectively and the first inverting integrator is used
In input signal w input and the input of the 4th phase inverter；The output end of 4th phase inverter is connecing hyperbolic just respectively
String function signal generator is used for input signal-w input and the input of the 5th inverting integrator；Hyperbolic sine function is believed
Output the 4th inverting integrator of termination of number generator is used for input signal-sinh input；SIN function signal generator
Output termination the 4th inverting integrator be used for input signal-sin input；
The input of output the 5th phase inverter of termination of 5th inverting integrator, the output termination of the 5th phase inverter is just
The input of string function signal generator.
2. five rank hyperchaotic systems of a kind of wide parameter region according to claim 1, it is characterised in that described first is anti-
Phase integral device includes the first operational amplifier（U1）, the first electric capacity（C1）, the 11st resistance（R11）, the 12nd resistance（R12）、
13rd resistance（R13）With the 14th resistance（R14）；First operational amplifier（U1）In-phase input end ground connection, it is anti-phase
Input connects the 11st resistance respectively（R11）, the 12nd resistance（R12）, the 13rd resistance（R13）With the 14th resistance
（R14）One end, the first electric capacity is connected between inverting input and output end（C1）；11st resistance（R11）, the 12nd
Resistance（R12）, the 13rd resistance（R13）With the 14th resistance（R14）The other end respectively constitute the first inverting integrator and be used for
Input signal-x ,-y ,-z and w four inputs, first operational amplifier（U1）Output end constitute the first anti-phase product
Divide the output end of device.
3. five rank hyperchaotic systems of a kind of wide parameter region according to claim 2, it is characterised in that described second is anti-
Phase integral device is identical with the structure of the first inverting integrator.
4. five rank hyperchaotic systems of a kind of wide parameter region according to claim 1, it is characterised in that the described 3rd is anti-
Phase integral device includes the 5th operational amplifier（U5）, the 3rd electric capacity（C3）, the 21st resistance（R21）With the 22nd resistance
（R22）；5th operational amplifier（U5）In-phase input end ground connection, inverting input connects the 21st resistance respectively
（R21）With the 22nd resistance（R22）One end, between inverting input and output end connect the 3rd electric capacity（C3）；Described
21 resistance（R21）With the 22nd resistance（R22）The other end respectively constitute the 3rd inverting integrator be used for input signal x
With y two inputs, the 5th operational amplifier（U5）Output end constitute the 3rd inverting integrator output end.
5. five rank hyperchaotic systems of a kind of wide parameter region according to claim 1, it is characterised in that the described 4th is anti-
Phase integral device includes the 7th operational amplifier（U7）, the 4th electric capacity（C4）, the 23rd resistance（R23）, the 24th resistance
（R24）With the 25th resistance（R25）；7th operational amplifier（U7）In-phase input end ground connection, inverting input point
Lian Jie not the 23rd resistance（R23）, the 24th resistance（R24）With the 25th resistance（R25）One end, inverting input
The 4th electric capacity is connected between output end（C4）；23rd resistance（R23）, the 24th resistance（R24）With the 20th
Five resistance（R25）The other end respectively constitute the 4th inverting integrator and be used for input signal-x ,-sin and-sinh three inputs
End, the 7th operational amplifier（U7）Output end constitute the 4th inverting integrator output end.
6. five rank hyperchaotic systems of a kind of wide parameter region according to claim 1, it is characterised in that the described 5th is anti-
Phase integral device includes the 9th operational amplifier（U9）, the 5th electric capacity（C5）With the 66th resistance（R66）；9th computing is put
Big device（U9）In-phase input end ground connection, inverting input connect the 66th resistance（R66）One end, inverting input with it is defeated
Go out the 5th electric capacity of connection between end（C5）；66th resistance（R66）The other end constitute the 5th inverting integrator it is defeated
Enter end, the 9th operational amplifier（U9）Output end constitute the 5th inverting integrator output end.
7. a kind of five rank hyperchaotic systems of wide parameter region according to claim 1, it is characterised in that the symbol letter
Number signal generator includes the 11st operational amplifier（U11）, the 12nd operational amplifier（U12）, the 19th resistance（R19）With
20th resistance（R20）；11st operational amplifier（U11）In-phase input end ground connection, output end connection the 19th electricity
Resistance（R19）；12nd operational amplifier（U12）In-phase input end ground connection, inverting input connect the 19th resistance
（R19）The other end, between inverting input and output end connect the 20th resistance（R20）；11st operational amplifier
（U11）Inverting input constitute sign function signal generator input, the 12nd operational amplifier（U12）Output end
Constitute the output end of sign function signal generator.
8. a kind of five rank hyperchaotic systems of wide parameter region according to claim 1, it is characterised in that the sinusoidal letter
Number signal generator includes the 13rd operational amplifier（U13）To the 17th operational amplifier（U17）, the 26th resistance
（R26）To the 39th resistance（R39）And the 5th diode（D5）To the tenth diode（D10）；And the 37th electricity
Resistance（R37）, the 38th resistance（R38）With the 39th resistance（R39）For variable resistor, wherein：
13rd operational amplifier（U13）In-phase input end ground connection, inverting input connect the 26th resistance（R26）
One end, between inverting input and output end connect the 27th resistance（R27）, output end the 28th resistance of connection
（R28）One end；Tenth four-operational amplifier（U14）In-phase input end ground connection, inverting input connection the 28th
Resistance（R28）The other end, between inverting input and output end connect the 29th resistance（R29）, output end connection the 3rd
Ten resistance（R30）；15th operational amplifier（U15）In-phase input end ground connection, inverting input connection the 30th electricity
Resistance（R30）The other end and the 34th resistance（R34）One end, between inverting input and output end connect the 31st electricity
Resistance（R31）, output end the 35th resistance of connection（R35）One end；16th operational amplifier（U16）Homophase input
End ground connection, inverting input connects the 32nd resistance（R32）One end, between inverting input and output end connect the 30th
Three resistance（R33）, output end the 34th resistance of connection（R34）The other end；
17th operational amplifier（U17）In-phase input end connect the 35th resistance respectively（R35）The other end,
Nine diodes（D9）Negative pole and the tenth diode（D10）Positive pole, inverting input connect the 36th resistance（R36）One
End, the 39th resistance（R39）One end and the 5th diode（D5）Negative pole, the 6th diode（D6）Positive pole, output end
Connect the 37th resistance（R37）One end, the 39th resistance（R39）The other end, the 7th diode（D7）Negative pole and
8th diode（D8）Positive pole；37th resistance（R37）Centre tap end connect the 9th diode（D9）Positive pole and
Tenth diode（D10）Negative pole；39th resistance（R39）Centre tap end connect the 5th diode（D5）Positive pole,
6th diode（D6）Negative pole, the 7th diode（D7）Positive pole and the 8th diode（D8）Negative pole；36th resistance
（R36）The other end connect the 38th resistance（R38）One end and its middle tap terminals；37th resistance（R37）It is another
One end and the 38th resistance（R38）Other end common ground；26th resistance（R26）The other end and the 30th
Two resistance（R32）The other end collectively form the input of SIN function signal generator, the 17th operational amplifier（U17）'s
Output end constitutes the output end of SIN function signal generator.
9. five rank hyperchaotic systems of a kind of wide parameter region according to claim 1, it is characterised in that the hyperbolic is just
String function signal generator includes the 18th operational amplifier（U18）To the 20th four-operational amplifier（U24）, the 40th resistance
（R40）To the 65th resistance（R65）, the 6th electric capacity（C6）To the 9th electric capacity（C9）, the first diode（D1）To the four or two pole
Pipe（D4）And first triode（Q1）To the 4th triode（Q4）；Wherein：
18th operational amplifier（U18）In-phase input end connect the 42nd resistance（R42）With the 43rd resistance
（R43）One end, inverting input connect the 40th resistance（R40）One end, is connected between inverting input and output end
41 resistance（R41）, output end the first diode of connection（D1）Negative pole and the second diode（D2）Positive pole；Described 4th
Ten resistance（R40）With the 43rd resistance（R43）The other end ground connection；19th operational amplifier（U19）It is same mutually defeated
Enter the 47th resistance of end connection（R47）One end, inverting input connect the first triode（Q1）With the second triode（Q2）
Emitter stage, between inverting input and output end connect the 46th resistance（R46）, output end the 48th resistance of connection
（R48）One end；47th resistance（R47）The other end ground connection；First triode（Q1）Colelctor electrode connect the 6th electric capacity
（C6）With the 44th resistance（R44）One end, the first triode（Q1）Base stage connect the 6th electric capacity（C6）The other end,
44 resistance（R44）The other end and the first diode（D1）Positive pole；Second triode（Q2）Colelctor electrode connection the 7th
Electric capacity（C7）With the 45th resistance（R45）One end, the second triode（Q2）Base stage connect the 7th electric capacity（C7）It is another
End, the 45th resistance（R45）The other end and the second diode（D2）Negative pole；20th operational amplifier（U20）
In-phase input end connect the 50th resistance（R50）One end, inverting input connect the 48th resistance（R48）It is another
End, connects the 49th resistance between inverting input and output end（R49）, output end the 51st resistance of connection（R51）'s
One end, the 50th resistance（R50）The other end ground connection；21st operational amplifier（U21）In-phase input end connection
56th resistance（R56）With the 58th resistance（R58）One end, inverting input connect the 55th resistance（R55）'s
One end, connects the 57th resistance between inverting input and output end（R57）, output end the 3rd diode of connection（D3）It is negative
Pole and the 4th diode（D4）Positive pole；58th resistance（R58）With the 55th resistance（R55）The other end ground connection；Institute
State the 22nd operational amplifier（U22）In-phase input end connect the 62nd resistance（R62）One end, inverting input connect
Connect the 3rd triode（Q3）With the 4th triode（Q4）Emitter stage, between inverting input and output end connect the 61st electricity
Resistance（R61）, output end the 63rd resistance of connection（R63）；62nd resistance（R62）The other end ground connection, the 3rd triode
（Q3）Colelctor electrode connect the 8th electric capacity（C8）With the 59th resistance（R59）One end, the 3rd triode（Q3）Base stage connect
Connect the 8th electric capacity（C8）The other end, the 59th resistance（R59）The other end and the 3rd diode（D3）Positive pole；Four or three
Pole pipe（Q4）Colelctor electrode connect the 9th electric capacity（C9）With the 60th resistance（R60）One end, the 4th triode（Q4）Base stage
Connect the 9th electric capacity（C9）The other end, the 60th resistance（R60）The other end and the 4th diode（D4）Negative pole；Described
23 operational amplifiers（U23）In-phase input end connect the 65th resistance（R65）One end, inverting input connection the
63 resistance（R63）The other end, between inverting input and output end connect the 64th resistance（R64）, output end company
Connect the 52nd resistance（R52）One end, the 65th resistance（R65）The other end ground connection；24th operation amplifier
Device（U24）In-phase input end connect the 54th resistance（R54）One end and the 52nd resistance（R52）The other end, instead
Phase input connects the 51st resistance（R51）The other end, between inverting input and output end connect the 53rd resistance
（R53）, the 54th resistance（R54）The other end ground connection；
42nd resistance（R42）With the 56th resistance（R56）The other end respectively constitute hyperbolic sine function signal
Generator is used for input signal-w and w two inputs, the 20th four-operational amplifier（U24）Output end constitute hyperbolic just
The output end of string function signal generator.
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