CN101800512B - Chaotic signal source with adjustable dynamic amplitude linearity - Google Patents
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Abstract
The invention relates to a chaotic signal source with adjustable dynamic amplitude linearity and a system with identical dynamic characteristics, comprising an inverse proportion circuit, a first integrating circuit, a second integrating circuit and a third integrating circuit, wherein the output ends of a third operational amplifier, a second operational amplifier and a first operational amplifier sequentially output three state variables (x, y, z) of the chaotic signal source; when the chaotic signal source works, the dynamic amplitudes of the three state variables (x, y, z) are linearly adjusted by adjusting the output voltage of a DC power supply, and the three state variables (x, y, z) are enabled to have the identical dynamic characteristics. Because the chaotic signal source has adjustable amplitude and frequency spectrums of different frequency ranges and the like under the precondition without changing the dynamic characteristics of an output signal, the chaotic signal source is indicated to have extensive application prospect and important application value in the high technology fields of chaotic radars, secret communication, electronic countermeasure, and the like.
Description
Technical field
The present invention relates to the chaos signal source that the adjustable and system of a kind of dynamic amplitude linearity has identical dynamics.
Background technology
The normal signal source can produce the different periodic signal of waveform, has been widely used in the information engineering field.The characteristics of periodic signal be convenient to modulation and demodulation synchronously, but be unfavorable for the requirement of special dimension such as information encryption.Chaotic signal has characteristics such as intrinsic stochasticity, initial value sensitiveness, broadband, ergodic and boundedness, can produce the broadband signal of similar white noise, so chaotic signal has a wide range of applications in fields such as information encryption, secure communication and chaotic radars.Chaos signal source is based on the important component part of the various information system modulation demodulation of chaos application, and circuit realizes that chaotic signal dynamic range linearity signal source adjustable, that dynamics is stable has important significance for theories and using value.
Since the famous meteorologist Lorenz of Massachusetts Institute Technology in 1963 proposed first chaos system, lot of domestic and foreign scholar proposed and has constructed a large amount of chaos systems.Over past ten years, people such as Sprott have found a class to have the low-dimensional chaos system of Jerk equation form based on the method for exhaustion by computer simulation technique, and its system's algebraic equation is simple, and nonlinear terms are various informative, have abundant dynamics, and circuit is easy to realize.These chaos systems generally when the regulating system parameter dynamics will change, even the dynamics of system changes not quite when the local modulation parameter, but be difficult to also guarantee that the dynamic range of exporting chaotic signal presents linear change.
The weak point of chaos system of the prior art is: can't realize that the adjustable and system of dynamic amplitude linearity has the chaos signal source of identical dynamics.
Summary of the invention
Technical problem to be solved by this invention provides the chaos signal source that the adjustable and system of a kind of dynamic amplitude linearity has identical dynamics.
For solving the problems of the technologies described above, the invention provides the chaos signal source that the adjustable and system of a kind of dynamic amplitude linearity has identical dynamics, comprising: oppositely ratio circuit, first integral circuit, second integral circuit and third integral circuit; Described first integral circuit comprises: the 4th resistance R 4 that first capacitor C 1 between the first amplifier A1, the reverse input end of being located at the first amplifier A1 and the output and an end link to each other with the reverse input end of the first amplifier A1; The other end of the 4th resistance R 4 links to each other with the positive pole of DC power supply V1, and first capacitor C 1 is parallel with first resistance R 1; Described second integral circuit comprises: the 3rd resistance R 3 that second capacitor C 2 between the second amplifier A2, the reverse input end of being located at the second amplifier A2 and the output and an end link to each other with the reverse input end of the second amplifier A2; The other end of the 3rd resistance R 3 links to each other with the output of the first amplifier A1; Described third integral circuit comprises: second resistance R 2 that the 3rd capacitor C 3 between the 3rd amplifier A3, the reverse input end of being located at the 3rd amplifier A3 and the output and an end link to each other with the reverse input end of the 3rd amplifier A3; The other end of second resistance R 2 links to each other with the output of the second amplifier A2; Described reverse ratio circuit comprises: the 7th resistance R 7 between four high guaily unit A4, the reverse input end of being located at four high guaily unit A4 and the output and be located at the output of four high guaily unit A4 and the reverse input end of the first amplifier A1 between the reverse input end of the 8th resistance R 8, the four high guaily unit A4 and the output of the second amplifier A2 between be provided with the 5th resistance R 5; The output of the 3rd amplifier A3 connects the negative electrode of the first diode D1 and the anode of the second diode D2 respectively after being connected in series the 6th resistance R 6, and the negative electrode of the anode of the first diode D1 and the second diode D2 connects the reverse input end of the first amplifier A1 and the reverse input end of four high guaily unit A4 respectively; The output of the 3rd amplifier A3, the second amplifier A2 and the first amplifier A1 is exported three state variable x as chaos signal source, y, z successively.
During chaos signal source work,,, and make described three state variable x, y and z have identical dynamics with the dynamic amplitude of linear regulation described three state variable x, y and z by regulating the output voltage of DC power supply V1;
The pairing circuit equation of above-mentioned chaos signal source is:
In the formula
Good effect of the present invention:
(1) the present invention has realized that the adjustable and system of dynamic amplitude linearity has the chaos signal source of identical dynamics, this chaos signal source is for containing nonlinear terms | the chaos system of the three rank constant coefficient differential equation forms of x|, and its Mathematical Modeling can be described as:
, a wherein, b and c are real number; If x represents displacement, then
Be the first derivative of x to the time, the speed of meaning;
Be the second dervative of x to the time, the acceleration of meaning;
Be three order derivatives of x to the time.Theory analysis and numerical simulation find that along with the variation of amplitude adjusted parameter c, the dynamic range of the chaos attractor that chaos signal source generates is linear change, and have identical dynamics (being constant Li Ya spectrum promise husband exponential spectrum).
(2) the analysis showed that, the dynamic range that the amplitude modulation parameter can Linear Control chaos signal source output signal, and do not influence the dynamics of chaos signal source self.Adopt the hardware circuit of chaos signal source of the present invention, through experimental verification this chaos signal source output signal amplitude in bigger dynamic range adjustable, pointed out the reason of amplitude modulation parameter to there are differences between the Experiment of Electrical Circuits of chaotic signal dynamic range control and the numerical simulation result.Find in addition, reduce the capacitance in the chaotic signal source circuit, the signal spectrum of output is moved to high frequency direction, show that this chaos signal source has the broadband character of different frequency range scope.Because this chaos signal source has advantages such as amplitude is adjustable under the prerequisite that does not change the output signal dynamics, the different frequency range frequency spectrum is adjustable, indicate that it has a wide range of applications and important use value in high-tech sectors such as chaotic radar, secure communication, electronic countermeasuress.
(3) the present invention proposes one and in this system, introduce an overall amplitude modulation parameter, propose and realized the chaos signal source that dynamic amplitude linearity is adjustable.When the amplitude modulation parameter changed, it is identical that the Liapunov exponent of chaos signal source keeps, and promptly dynamics does not change.Change the dynamic range that to control the chaos signal source output signal easily by the amplitude modulation parameter.Results of study such as theory analysis, numerical simulation and Experiment of Electrical Circuits have consistency preferably.
Description of drawings
For the easier quilt of content of the present invention is clearly understood, below the specific embodiment and in conjunction with the accompanying drawings of basis, the present invention is further detailed explanation, wherein
Fig. 1 (a) is the projection of chaos attractor on the x-y plane of the generation of chaos signal source;
Fig. 1 (b) is the projection of chaos attractor on the x-z plane of the generation of chaos signal source;
Fig. 2 (a) is the time domain waveform of the variable y of chaos signal source;
Fig. 2 (b) is the time domain waveform of the variable z of chaos signal source;
Fig. 3 (a) is the Lyapunov exponents that chaos signal source changes with the amplitude modulation parameter c;
Fig. 3 (b) is the bifurcation graphs of chaos signal source with the variable x of amplitude modulation parameter c variation;
Fig. 3 (c) is the bifurcation graphs of chaos signal source with the variable y of amplitude modulation parameter c variation;
Fig. 3 (d) is the bifurcation graphs of chaos signal source with the variable z of amplitude modulation parameter c variation;
Fig. 4 (a) is the projection of chaos attractor on the x-y plane of the generation of parameter c=2 o'clock chaos signal source;
Fig. 4 (b) is the projection of chaos attractor on the x-y plane of the generation of parameter c=8 o'clock chaos signal source;
Fig. 5 is the circuit theory diagrams of the adjustable chaos signal source of the dynamic amplitude linearity among the embodiment;
Fig. 6 (a) is the projection of chaos attractor on the x-y plane of the generation of parameter c=4 o'clock chaos signal source;
Fig. 6 (b) is the projection of chaos attractor on the x-z plane of the generation of parameter c=4 o'clock chaos signal source;
Fig. 7 (a) is the time domain waveform of the variable y of parameter c=4 o'clock chaos signal source;
Fig. 7 (b) is the time domain waveform of the variable z of parameter c=4 o'clock chaos signal source;
Fig. 8 is the projection of chaos attractor on the x-z plane of the generation of parameter c=2 o'clock chaos signal source.
Embodiment
See Fig. 1-8, the Mathematical Modeling of the chaos signal source that a kind of dynamic amplitude linearity of present embodiment is adjustable can be described as:
A wherein, b and c are real number.Order
, formula (2) can be rewritten as following form:
Order
, can solve formula (3) and have 2 balance point: S1:(-c/b, 0,0), S2:(c/b, 0,0).Balance point S*=(x*, y* z*) carry out linearization process to formula (3), its Jacobian matrix be:
The characteristic root equation that can be obtained system (3) by formula (4) is:
For balance point S
1: (c/b, 0,0), its characteristic root equation can be reduced to
, by Louth-Hall dimension thatch criterion as can be known, work as a, b〉and 0, during and a＜b, S
1Be unsettled.Work as a=0.4, b=0.81 during c=4, obtains S
1: the characteristic root of (4.9383,0,0) is
Because
For a pair of real part is positive conjugation compound radical, and
Less than zero, so S
1Be the balance point of index 2, the balance point with index 2 is the necessary condition that system's path forms scrollwork.
For balance point S
2: (c/b, 0,0), the characteristic root equation after it is simplified is
, learn by Louth-Hall dimension thatch criterion, work as a, b〉0, S
2Be unsettled.Work as a=0.4, b=0.81, during c=4, balance point S
2: the characteristic root of (4.9383,0,0) is
, because
For a pair of real part is negative conjugation compound radical, and
Greater than zero, so S
2Be the balance point of index 1, system's path is at balance point S
2Can not form scrollwork.
Work as a=0.4, b=0.81, during c=4, chaos signal source can generate chaos attractor as shown in Figure 1.Corresponding Liapunov exponent is LE
1=0.0902, LE
2=0.0024, LE
3=-0.4926, its Lyapunov dimension d
L=2.1880.The time domain waveform of chaos signal source output signal as shown in Figure 2, its path is acyclic, seems to be random behavior.From the phase rail figure of attractor, Liapunov exponent and time domain waveform etc. can judge that chaos signal source is a chaos, and the topological structure of chaos attractor has the single-blade circulus.
By calculating the Lyapunov exponents that chaos signal source changes with parameter c, can the quantitative observation parameter c change influence to the dynamics of chaos signal source.Get chaos signal source parameter a=0.4, b=0.81, (x, y z) are (0,0,0) to initial condition, and the Lyapunov exponents that is changed with parameter c by Jacobian matrix formula (4) numerical computations is shown in Fig. 3 (a).By Fig. 3 (a) as seen, three Liapunov exponents of chaos signal source are respectively LE
1=0.0902, LE
2=0.0024, LE
3=-0.4926, do not change with parameter c.This explanation is stablized at the dynamics that keeps chaos signal source can be by adjusting the dynamic range that parameter c changes the output chaotic signal under the constant situation.
Three state variable x of chaos signal source output, y, bifurcation graphs such as Fig. 3 (b) that z changes with parameter c are (c) and (d).Observe Fig. 3 (b), (c) and (d) can find, in the whole interval that parameter c changes, chaos signal source is a chaotic oscillation, the operation path of the chaotic signal of exporting when increasing with the parameter c dynamic range of projection in the plane is linear increase, this explanation parameter c has overall linear amplitude modulation function to chaos signal source, and can keep dynamics constant.This notable feature of parameter c meets the normal signal source fully amplitude output signal is adjusted the requirement of function, and this paper is defined as the dynamic amplitude linearity adjustable parameter of chaos signal source to parameter c, is called for short the amplitude modulation parameter.Above-mentioned the analysis showed that, chaos signal source amplitude output signal linearity is adjustable, has important use to be worth in information engineering fields such as chaotic radar, electronic countermeasuress.
Keep a=0.4, b=0.81 is constant, and parameter c gets 2 and respectively at 8 o'clock, and the projection of chaos attractor on the x-y plane that system (3) produces is respectively as Fig. 4 (a) with (b).The dynamic range of the chaos attractor shown in Fig. 4 and Fig. 1 (a) can be listed in the table 1.Comparison diagram 4, Fig. 1 (a) and analytical table 1 data learn that when parameter c difference value, the topological structure of chaos attractor remains unchanged, and the amplitude size of chaotic signal changes in proportion synchronously.
The dynamic range [0049] of table 1 chaos signal source output signal
Chaos signal source circuit design based on the Jerk equation form is comparatively simple, functions such as the plus-minus of the single amplifier chip realization of selection model OP07CP chaos signal source Mathematical Modeling and calculus computing, this chip adopts dual power supply, maximum supply power voltage is ± 22V, have bigger out-put dynamic range, be convenient in experiment, observe the adjusting range of amplitude modulation parameter the chaos signal source output signal; Select direct current variable voltage source V
1Realize the dynamic amplitude regulatory function of chaos signal source; Nonlinear terms | the function of x| is realized by combinations such as the diode of two model IN4001 and single amplifier chips.The circuit theory diagrams of the chaos signal source that this paper proposed as shown in Figure 5.
The pairing circuit equation of Fig. 5 can be listed as the following form of being write as:
1/R in the formula
1C, 1/R
2C and V
1/ R
3C corresponds respectively to parameter a in the Mathematical Modeling of chaos signal source, the value of b and c.Can adjust the frequency of oscillation of chaos signal source easily by the value that changes capacitor C among Fig. 5.Selecting circuit parameters R=1k Ω, C=1 μ F, R
1=2.49k Ω, R
2=1.21k Ω utilizes the Tektronix digital storage oscilloscope to carry out the observation of circuit output signal.Work as voltage source V
1Be output as 4V and be amplitude adjusted parameter c=4 o'clock, the phase rail figure of chaos signal source and the time domain waveform of output signal are respectively shown in Fig. 6 and 7.Can observe three state variable x thus, y, the dynamic range of z output signal is respectively: 4.2V, 3.2V and 3.2V.It should be noted that, in order to observe y variable output signal in Fig. 6 circuit, can be by realizing at-external the reverser of y output.
Change voltage source V
1Be output as 2V, i.e. fixedly amplitude modulation parameter c=2, the phase rail figure of chaos signal source signal source output as shown in Figure 8, three state variable item x here, y, the dynamic range of z output signal is respectively: 3.0V, 2.0V and 2.0V.Comparison diagram 6 and Fig. 8 can find, the topological structure unanimity of chaos signal source phase rail figure, and work is corresponding to be changed and dynamic range changes with the amplitude modulation parameter.Need to prove that there are certain difference in Experiment of Electrical Circuits and numerical simulation result, mainly is that diode has the threshold voltage of 0.6V to cause approximately in the side circuit.But experiment output result is enough to illustrate that there is the overall linear amplitude modulation function with engineering significance in the chaos signal source that this paper proposes.
The foregoing description only is for example of the present invention clearly is described, and is not to be qualification to embodiments of the present invention.For those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.Here need not also can't give exhaustive to all execution modes.
Claims (3)
1. the chaos signal source that dynamic amplitude linearity is adjustable is characterized in that comprising: reverse ratio circuit, first integral circuit, second integral circuit and third integral circuit;
Described first integral circuit comprises: first amplifier (A1), be located at the 4th resistance (R4) that the reverse input end of first amplifier (A1) and first electric capacity (C1) between the output and an end link to each other with the reverse input end of first amplifier (A1); The other end of the 4th resistance (R4) links to each other with the positive pole of DC power supply (V1), and first electric capacity (C1) is parallel with first resistance (R1);
Described second integral circuit comprises: second amplifier (A2), be located at the 3rd resistance (R3) that the reverse input end of second amplifier (A2) and second electric capacity (C2) between the output and an end link to each other with the reverse input end of second amplifier (A2); The other end of the 3rd resistance (R3) links to each other with the output of first amplifier (A1);
Described third integral circuit comprises: the 3rd amplifier (A3), be located at second resistance (R2) that the reverse input end of the 3rd amplifier (A3) and the 3rd electric capacity (C3) between the output and an end link to each other with the reverse input end of the 3rd amplifier (A3); The other end of second resistance (R2) links to each other with the output of second amplifier (A2);
Described reverse ratio circuit comprises: four high guaily unit (A4), be located at the reverse input end of four high guaily unit (A4) and the 7th resistance (R7) between the output and be located at the output of four high guaily unit (A4) and the reverse input end of first amplifier (A1) between the 8th resistance (R8), be provided with the 5th resistance (R5) between the output of the reverse input end of four high guaily unit (A4) and second amplifier (A2);
The output of the 3rd amplifier (A3) connects the negative electrode of first diode (D1) and the anode of second diode (D2) respectively after being connected in series the 6th resistance (R6), and the negative electrode of the anode of first diode (D1) and second diode (D2) connects the reverse input end of first amplifier (A1) and four high guaily unit (A4) respectively;
The output of the 3rd amplifier (A3), second amplifier (A2) and first amplifier (A1) is exported three state variable x as chaos signal source, y, z successively;
During chaos signal source work,,, and make described three state variable x, y and z have identical dynamics with the dynamic amplitude of linear regulation described three state variable x, y and z by regulating the output voltage of DC power supply (V1);
The pairing circuit equation of above-mentioned chaos signal source is:
In the formula
2. the adjustable chaos signal source of dynamic amplitude linearity according to claim 1 is characterized in that: the resistance of the 3rd resistance (R3), the 4th resistance (R4), the 5th resistance (R5) and the 6th resistance (R6) equates.
3. the adjustable chaos signal source of dynamic amplitude linearity according to claim 1, it is characterized in that: the capacitance of described first electric capacity (C1), second electric capacity (C2) and the 3rd electric capacity (C3) equates, and, adjust described three state variable x, the y of chaos signal source and the frequency of oscillation of z by regulating the capacitance of each electric capacity simultaneously.
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| CN102142956A (en) * | 2011-04-20 | 2011-08-03 | 河南化工职业学院 | Two-dimensional chaotic circuit and two-dimensional chaotic privacy communication system thereof |
| CN102611388B (en) * | 2012-03-26 | 2015-04-22 | 常州大学 | One-parameter robust chaotic signal source |
| CN103066922B (en) * | 2012-12-17 | 2015-06-24 | 常州大学 | Memory system chaotic signal generator |
| CN103188069A (en) * | 2013-01-09 | 2013-07-03 | 王少夫 | Three-dimensional chaotic system with adjustable amplitudes |
| CN105245204A (en) * | 2015-08-26 | 2016-01-13 | 韩敬伟 | Five-item quasi-period spherical oscillation system and circuit thereof |
| CN105227159A (en) * | 2015-08-26 | 2016-01-06 | 韩敬伟 | A kind of spherical five quasi-periodic oscillation systems and circuit |
| CN107483176B (en) * | 2016-05-22 | 2020-06-05 | 台州市牛诺电子商务有限公司 | Circuit for linearizing Sprott B chaotic system into quadratic term |
| CN105846991B (en) * | 2016-06-06 | 2018-11-23 | 南京信息工程大学 | Simple three-dimensional width-adjustable chaos signal generator |
| CN106059745B (en) * | 2016-06-06 | 2019-01-08 | 南京信息工程大学 | More system amplitude modulation chaos JERK circuits |
| CN105871535B (en) * | 2016-06-06 | 2018-09-14 | 南京信息工程大学 | A kind of width-adjustable hyperchaos signal source |
| CN110198212B (en) * | 2019-03-08 | 2021-07-27 | 天津大学 | Amplitude-adjustable balance point switchable chaotic signal source generation device |
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Effective date of registration: 20130725 Address after: 226600, Jiangsu County, Nantong City, Haian province Haian City Industrial Park, the Eastern District Patentee after: Nantong Aorun Building Material Technology Co., Ltd. Patentee after: Jiangsu University of Technology Address before: 213001 Changzhou Province in the Clock Tower District, Jiangsu, Wu Road, No. 1801 Patentee before: Jiangsu Teachers University of Technology |