CN104753660B - three-dimensional chaotic system circuit - Google Patents
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Abstract
The invention discloses a kind of three-dimensional chaotic system circuit, including first, second, and third channel circuit.First passage circuit is made up of multiplier A1, multiplier A2, inverting integrator U1A and resistance R13 and R14, second channel circuit is made up of multiplier A3, phase inverter U2A, phase inverter U3A, inverting integrator U4A and resistance R23, R24, R25, R26, R27 and R28, and third channel circuit is made up of multiplier A4, phase inverter U5A, inverting integrator U6A and resistance R33, R34, R35 and R36.The present invention can realize six kinds of three-dimensional chaotic system circuits by changing element in circuit unit and device parameter values, and every kind of chaos system circuit has respective chaotic dynamics behavior.The invention has the advantages that：1. circuit structure is simple, is easy to hardware realization；2. suitable for the experimental teaching of nonlinear system circuit, and it can apply in information security fields such as image concealing, secret communications.
Description
Technical field
The present invention relates to three-dimensional chaotic system circuit, belongs to the technical field that chaos signal generator designs.
Background technology
Nonlinear science is forward position and the focus of world today's science, is related to natural science and numerous necks of social science
Domain, Chaos in Some can be described as one of key problem of nonlinear science.Chaos as a kind of complicated nonlinear motion behavior,
It is widely used in fields such as biology, chemistry, engineering science and informatics.Turbulent phenomenon is described since 1963
After Lorenz chaos systems are suggested, a variety of different chaos systems are suggested in succession, and the nonlinear terms of most chaos systems
It is multiplied, the chaos system being multiplied with three state variables is studied fresh few for two state variables.
Chaos system of the design with complex nonlinear item, and its integer rank chaos system is expanded into fractional order chaos system
System, the dynamics of system can be reflected exactly.Further, by changing chaos system exponent number（Change chaos system
Circuit unit structure）, can be designed that the chaos system circuit of different rank.If such chaos system circuit is applied to non-thread
Property circuit experimental teaching in, by increasing capacitance it is possible to increase to the intuitive of nonlinear circuit design, and such chaos system circuit is being protected
The close communications field has good application prospect.
The content of the invention
It is an object of the invention to provide six kinds of chaos system circuits, its system output signal can apply it is hidden in image
In the fields such as Tibetan, secret communication, and the chaos system circuit can apply to nonlinear circuit teaching experiment.
The technical solution adopted by the present invention is：
Three-dimensional chaotic system circuit, it is made up of three channel circuits：First passage circuit by multiplier A1, multiplier A2,
Inverting integrator U1A and resistance R13 and R14 composition, second channel circuit is by multiplier A3, phase inverter U2A, phase inverter
U3A, inverting integrator U4A and resistance R23, R24, R25, R26, R27 and R28 composition, third channel circuit by multiplier A4,
Phase inverter U5A, inverting integrator U6A and resistance R33, R34, R35 and R36 composition；The output signal of first passage circuit is anti-
Input is fed to, connection resistance R14 is also used as multiplier A3 in second channel circuit as input signal all the way, the output signal
Input signal all the way, the output signal is also connected with multiplier A4 and acts on third channel circuit；The output of second channel circuit
Signal feeds back to input, and as input signal all the way, the output signal is also used as in first passage circuit to be multiplied connection resistance R23
Musical instruments used in a Buddhist or Taoist mass A1 input signal all the way, the output signal are also connected with multiplier A4 and act on third channel circuit；Third channel circuit
Output signal connection resistance R36 act on third channel circuit, the output signal is also as multiplier A1's and multiplier A2
Input signal all the way, the output signal are also connected with multiplier A3 and act on second channel circuit.
The inverting integrator includes phase inverter and circuit unit, when circuit unit is single electric capacity, three-dimensional chaos system
System circuit is integer rank three-dimensional chaotic system circuit；Work as circuit unit, connected first by resistance capacitance parallel circuit with electric capacity, so
Afterwards during composition in parallel with a resistor, three-dimensional chaotic system circuit is fractional order three-dimensional chaotic system circuit.The exponent number of inverting integrator
For 0.95-1, six kinds of chaos system circuits are formed.First passage circuit mid-score rank inverting integrator U1A output ends are X signal；
Second channel circuit mid-score rank inverting integrator U4A output ends are Y-signal；Third channel circuit mid-score rank inverting integrator
U6A output ends are Z signals.
The present invention devises new fractional order circuit unit, is successfully realized the circuit that fractional order exponent number is 0.95 to 0.99
Unit, and six kinds of fractional order chaotic system circuits are realized using analog circuit, such chaos system has complicated dynamics
Behavior, therefore the chaos system is applied in image encryption, secret communication field, it is possible to increase disguised, the anti-decoding of enhancing
Ability.
Brief description of the drawings
Fig. 1 is the basic circuit diagram of the present invention；
Fig. 2 is integer rank chaos system circuit diagram；
Fig. 3 is the chaos system circuit diagram that fractional order exponent number is 0.95；
Fig. 4 is the chaos system circuit diagram that fractional order exponent number is 0.96；
Fig. 5 is the chaos system circuit diagram that fractional order exponent number is 0.97；
Fig. 6 is the chaos system circuit diagram that fractional order exponent number is 0.98；
Fig. 7 is the chaos system circuit diagram that fractional order exponent number is 0.99；
Fig. 8 is integer rank chaos system circuit X-Y phase-plane diagrams；
Fig. 9 is the chaos system circuit X-Y phase-plane diagrams that fractional order exponent number is 0.95；
Figure 10 is the chaos system circuit X-Y phase-plane diagrams that fractional order exponent number is 0.96；
Figure 11 is the chaos system circuit X-Y phase-plane diagrams that fractional order exponent number is 0.97；
Figure 12 is the chaos system circuit X-Y phase-plane diagrams that fractional order exponent number is 0.98；
Figure 13 is the chaos system circuit X-Y phase-plane diagrams that fractional order exponent number is 0.99.
Embodiment
The present invention is described in further detail with specific implementation below in conjunction with the accompanying drawings.
Mathematical modeling involved in the present invention is as follows：
In formula, x, y, z are state variable, and q is exponent number, and as q=1, system is integer rank chaos system, each differential equation
Parameter be determination value.
Artificial circuit involved in the present invention is made up of first, second, and third channel circuit, and first, second, third is logical
Road circuit realizes first, second, third function in above-mentioned mathematical modeling respectively.
As shown in Figure 1：Three-dimensional chaotic system circuit of the present invention, first passage circuit mid-score rank inverting integrator U1A are defeated
It is X signal to go out end；Second channel circuit mid-score rank inverting integrator U4A output ends are Y-signal；Third channel circuit mid-score
Rank inverting integrator U6A output ends are Z signals.In circuit, resistance capacitance is standard component, and the model of amplifier is
LT082CM；VCC numerical value is 15V.
Three-dimensional chaotic system circuit, it is made up of three channel circuits：First passage circuit by multiplier A1, multiplier A2,
Inverting integrator U1A and resistance R13 and R14 composition, second channel circuit is by multiplier A3, phase inverter U2A, phase inverter
U3A, inverting integrator U4A and resistance R23, R24, R25, R26, R27 and R28 composition, third channel circuit by multiplier A4,
Phase inverter U5A, inverting integrator U6A and resistance R33, R34, R35 and R36 composition；The output signal of first passage circuit is anti-
Input is fed to, connection resistance R14 is also used as multiplier A3 in second channel circuit as input signal all the way, the output signal
Input signal all the way, the output signal is also connected with multiplier A4 and acts on third channel circuit；The output of second channel circuit
Signal feeds back to input, and connection resistance R23 is as input signal, also one as multiplier A1 in first passage circuit all the way
Road input signal, the output signal are also connected with multiplier A4 and act on third channel circuit；The output signal of third channel circuit
Connection resistance R36 acts on third channel circuit, the also input signal all the way as multiplier A1 and multiplier A2, output letter
Number being also connected with multiplier A3 acts on second channel circuit.
As shown in Figure 2：Described integer rank chaos system circuit, is made up of, first first, second, and third channel circuit
Channel circuit is made up of multiplier A1, multiplier A2, phase inverter U1A, electric capacity C11 and resistance R13 and R14, second channel electricity
It route multiplier A3, phase inverter U2A, phase inverter U3A, phase inverter U4A, electric capacity C21 and resistance R23, R24, R25, R26, R27
With R28 form, third channel circuit by multiplier A4, phase inverter U5A, phase inverter U6A, electric capacity C31 and resistance R33, R34,
R35 and R36 compositions；The output signal of first passage circuit feeds back to input, and connection resistance R14 is used as input signal all the way,
All the way input signal of the output signal also as multiplier A3 in second channel circuit, the output signal are also connected with multiplier A4
Act on third channel circuit；The output signal of second channel circuit feeds back to input, and connection resistance R23 is used as to be inputted all the way
Signal, the also input signal all the way as multiplier A1 in first passage circuit, the output signal are also connected with multiplier A4 effects
In third channel circuit；The output signal connection resistance R36 of third channel circuit acts on third channel circuit, also as multiplication
Device A1 and multiplier A2 input signal all the way, the output signal are also connected with multiplier A3 and act on second channel circuit.
As shown in Figure 3：Described fractional order exponent number is 0.95 chaos system circuit, by first, second, and third passage
Circuit forms, and first passage circuit is by multiplier A1, multiplier A2,0.95 rank inverting integrator U1A and resistance R13 and R14
Composition, second channel circuit is by multiplier A3, phase inverter U2A, phase inverter U3A, 0.95 rank inverting integrator U4A and resistance
R23, R24, R25, R26, R27 and R28 are formed, and third channel circuit is by multiplier A4, phase inverter U5A, the anti-phase integration of 0.95 rank
Device U6A and resistance R33, R34, R35 and R36 composition；The output signal of first passage circuit feeds back to input, connects resistance
R14 is as input signal all the way, and all the way input signal of the output signal also as multiplier A3 in second channel circuit, this is defeated
Go out signal and be also connected with multiplier A4 to act on third channel circuit；The output signal of second channel circuit feeds back to input, even
Connecting resistance R23 is as input signal, the also input signal all the way as multiplier A1 in first passage circuit all the way, output letter
Number being also connected with multiplier A4 acts on third channel circuit；The output signal connection resistance R36 of third channel circuit acts on the
Triple channel circuit, the also input signal all the way as multiplier A1 and multiplier A2, the output signal are also connected with multiplier A3 works
For second channel circuit.
As shown in Figure 4：Described fractional order exponent number is 0.96 chaos system circuit, by first, second, and third passage
Circuit forms, and first passage circuit is by multiplier A1, multiplier A2,0.96 rank inverting integrator U1A and resistance R13 and R14
Composition, second channel circuit is by multiplier A3, phase inverter U2A, phase inverter U3A, 0.96 rank inverting integrator U4A and resistance
R23, R24, R25, R26, R27 and R28 are formed, and third channel circuit is by multiplier A4, phase inverter U5A, the anti-phase integration of 0.96 rank
Device U6A and resistance R33, R34, R35 and R36 composition；The output signal of first passage circuit feeds back to input, connects resistance
R14 is as input signal all the way, and all the way input signal of the output signal also as multiplier A3 in second channel circuit, this is defeated
Go out signal and be also connected with multiplier A4 to act on third channel circuit；The output signal of second channel circuit feeds back to input, even
Connecting resistance R23 is as input signal, the also input signal all the way as multiplier A1 in first passage circuit all the way, output letter
Number being also connected with multiplier A4 acts on third channel circuit；The output signal connection resistance R36 of third channel circuit acts on the
Triple channel circuit, the also input signal all the way as multiplier A1 and multiplier A2, the output signal are also connected with multiplier A3 works
For second channel circuit.
As shown in Figure 5：Described fractional order exponent number is 0.97 chaos system circuit, by first, second, and third passage
Circuit forms, and first passage circuit is by multiplier A1, multiplier A2,0.97 rank inverting integrator U1A and resistance R13 and R14
Composition, second channel circuit is by multiplier A3, phase inverter U2A, phase inverter U3A, 0.97 rank inverting integrator U4A and resistance
R23, R24, R25, R26, R27 and R28 are formed, and third channel circuit is by multiplier A4, phase inverter U5A, the anti-phase integration of 0.97 rank
Device U6A and resistance R33, R34, R35 and R36 composition；The output signal of first passage circuit feeds back to input, connects resistance
R14 is as input signal all the way, and all the way input signal of the output signal also as multiplier A3 in second channel circuit, this is defeated
Go out signal and be also connected with multiplier A4 to act on third channel circuit；The output signal of second channel circuit feeds back to input, even
Connecting resistance R23 is as input signal, the also input signal all the way as multiplier A1 in first passage circuit all the way, output letter
Number being also connected with multiplier A4 acts on third channel circuit；The output signal connection resistance R36 of third channel circuit acts on the
Triple channel circuit, the also input signal all the way as multiplier A1 and multiplier A2, the output signal are also connected with multiplier A3 works
For second channel circuit.
As shown in Figure 6：Described fractional order exponent number is 0.98 chaos system circuit, by first, second, and third passage
Circuit forms, and first passage circuit is by multiplier A1, multiplier A2,0.98 rank inverting integrator U1A and resistance R13 and R14
Composition, second channel circuit is by multiplier A3, phase inverter U2A, phase inverter U3A, 0.98 rank inverting integrator U4A and resistance
R23, R24, R25, R26, R27 and R28 are formed, and third channel circuit is by multiplier A4, phase inverter U5A, the anti-phase integration of 0.98 rank
Device U6A and resistance R33, R34, R35 and R36 composition；The output signal of first passage circuit feeds back to input, connects resistance
R14 is as input signal all the way, and all the way input signal of the output signal also as multiplier A3 in second channel circuit, this is defeated
Go out signal and be also connected with multiplier A4 to act on third channel circuit；The output signal of second channel circuit feeds back to input, even
Connecting resistance R23 is as input signal, the also input signal all the way as multiplier A1 in first passage circuit all the way, output letter
Number being also connected with multiplier A4 acts on third channel circuit；The output signal connection resistance R36 of third channel circuit acts on the
Triple channel circuit, the also input signal all the way as multiplier A1 and multiplier A2, the output signal are also connected with multiplier A3 works
For second channel circuit.
As shown in Figure 7：Described fractional order exponent number is 0.99 chaos system circuit, by first, second, and third passage
Circuit forms, and first passage circuit is by multiplier A1, multiplier A2,0.99 rank inverting integrator U1A and resistance R13 and R14
Composition, second channel circuit is by multiplier A3, phase inverter U2A, phase inverter U3A, 0.99 rank inverting integrator U4A and resistance
R23, R24, R25, R26, R27 and R28 are formed, and third channel circuit is by multiplier A4, phase inverter U5A, the anti-phase integration of 0.99 rank
Device U6A and resistance R33, R34, R35 and R36 composition；The output signal of first passage circuit feeds back to input, connects resistance
R14 is as input signal all the way, and all the way input signal of the output signal also as multiplier A3 in second channel circuit, this is defeated
Go out signal and be also connected with multiplier A4 to act on third channel circuit；The output signal of second channel circuit feeds back to input, even
Connecting resistance R23 is as input signal, the also input signal all the way as multiplier A1 in first passage circuit all the way, output letter
Number being also connected with multiplier A4 acts on third channel circuit；The output signal connection resistance R36 of third channel circuit acts on the
Triple channel circuit, the also input signal all the way as multiplier A1 and multiplier A2, the output signal are also connected with multiplier A3 works
For second channel circuit.
Above-mentioned six kinds of three-dimensional chaotic system circuits, it is characterised in that：When described fractional order exponent number is 0.95, circuit list
Resistance and capacitance in member are respectively：0.0191M Ω, 8.9101M Ω, 3.6487 μ F and 0.99213 μ F；When described fraction
When rank exponent number is 0.96, resistance and capacitance in circuit unit are respectively：6.1435K Ω, 9.1192M Ω, 3.5943 μ F and
0.972μF；When described fractional order exponent number is 0.97, resistance and capacitance in circuit unit are respectively：914.102Ω、
9.3303M Ω, 3.557 μ F and 0.9516 μ F；When described fractional order exponent number is 0.98, resistance and electric capacity in circuit unit
Value is respectively：1.8277K Ω, 870.625M Ω, 3.8451 μ F and 1.02153 μ F；When described fractional order exponent number is 0.99,
Resistance and capacitance in circuit unit are respectively：0.00198 Ω, 95.5402M Ω, 3.5637 μ F and 0.9316 μ F.When described
Exponent number when being 1, the capacitance in circuit unit is 1 μ F.
Claims (1)
1. three-dimensional chaotic system circuit, it is characterised in that：The circuit is made up of three channel circuits：First passage circuit is by multiplication
Device A1, multiplier A2, inverting integrator U1A and resistance R13 and R14 composition, second channel circuit is by multiplier A3, anti-phase
Device U2A, phase inverter U3A, inverting integrator U4A and resistance R23, R24, R25, R26, R27 and R28 composition, third channel electricity
It route multiplier A4, phase inverter U5A, inverting integrator U6A and resistance R33, R34, R35 and R36 composition；First passage circuit
Output signal feed back to input, connection resistance R14 is as input signal all the way, and the output signal is also as second channel electricity
Multiplier A3 input signal all the way, the output signal are also connected with multiplier A4 and act on third channel circuit in road；Second is logical
The output signal of road circuit feeds back to input, and connection resistance R23 is also used as first as input signal all the way, the output signal
Multiplier A1 input signal all the way, the output signal are also connected with multiplier A4 and act on third channel circuit in channel circuit；
The output signal connection resistance R36 of third channel circuit acts on third channel circuit, and the output signal is also used as multiplier A1
With multiplier A2 input signal all the way, the output signal is also connected with multiplier A3 and acts on second channel circuit；
Wherein, inverting integrator includes phase inverter and circuit unit, when circuit unit is single electric capacity, three-dimensional chaotic system electricity
Road is integer rank three-dimensional chaotic system circuit；When circuit unit connected by resistance capacitance parallel circuit with electric capacity, again with resistance simultaneously
During connection composition, three-dimensional chaotic system circuit is fractional order three-dimensional chaotic system circuit；
The fractional order exponent number of the fractional order three-dimensional chaotic system circuit is 0.95-0.99：When fractional order exponent number is 0.95, electricity
Resistance and capacitance in the unit of road are respectively：0.0191M Ω, 8.9101M Ω, 3.6487 μ F and 0.99213 μ F；Work as fractional order
When exponent number is 0.96, resistance and capacitance in circuit unit are respectively：6.1435K Ω, 9.1192M Ω, 3.5943 μ F and
0.972μF；When fractional order exponent number is 0.97, resistance and capacitance in circuit unit are respectively：914.102Ω、9.3303M
Ω, 3.557 μ F and 0.9516 μ F；When fractional order exponent number is 0.98, resistance and capacitance in circuit unit are respectively：
1.8277K Ω, 870.625M Ω, 3.8451 μ F and 1.02153 μ F；When fractional order exponent number is 0.99, the electricity in circuit unit
Resistance and capacitance are respectively：0.00198 Ω, 95.5402M Ω, 3.5637 μ F and 0.9316 μ F.
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| CN105939103A (en) * | 2015-09-18 | 2016-09-14 | 重庆邮电大学 | Fractional order chaotic circuit applicable to PWM generator |
| CN105938672A (en) * | 2015-09-18 | 2016-09-14 | 重庆邮电大学 | Chaotic system circuit applied to non-linear circuit teaching experiment |
| CN105721138B (en) * | 2016-04-12 | 2019-03-22 | 天津科技大学 | A kind of secret communication method and analog circuit based on four wing chaos system of fractional order |
| CN107566109B (en) * | 2017-10-16 | 2023-06-13 | 中船第九设计研究院工程有限公司 | Three-dimensional chaotic circuit |
| CN108337081B (en) * | 2018-03-21 | 2019-09-17 | 齐鲁理工学院 | One kind containing constant term three-dimensional chaos circuit three times |
| CN110113146B (en) * | 2019-06-04 | 2022-04-29 | 齐鲁理工学院 | Analog circuit of fractional order chaotic system |
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