CN105845004A - Chua's circuit realized based on hysteresis function - Google Patents
Chua's circuit realized based on hysteresis function Download PDFInfo
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- CN105845004A CN105845004A CN201610345238.7A CN201610345238A CN105845004A CN 105845004 A CN105845004 A CN 105845004A CN 201610345238 A CN201610345238 A CN 201610345238A CN 105845004 A CN105845004 A CN 105845004A
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Abstract
The invention relates to a Chua's circuit realized based on a hysteresis function. The Chua's circuit is composed of six operational amplifiers, fourteen resistors, and three capacitors. The operational amplifiers A1, A2, and A3 form an anti-phase integrator and the output terminals output chaotic signals X, Y, and Z; the operational amplifiers A4 and A6 form an inverting amplifier; and the operational amplifier A5 forms a hysteresis function circuit. When the circuit is in use, oscillograms of the X, Y, and Z can be observed on a common oscilloscope and X-Y, X-Z, and Y-Z phase graphs can be observed. The chaotic system of the Chua's circuit is enriched. The Chua's circuit is suitable for the chaotic science of the university, the experiment teaching and demonstration, science popularization, and experiment demonstration and the like. With the circuit, various chaotic wave forms, phase graphs, and chaotic development curves can be displayed. The circuit can be applied to the voice-analog-signal secret communication system widely.
Description
Technical field
The invention belongs to nonlinear circuit and system, often claim chaos circuit, be specifically related to what a kind of hysteresis function realized
Cai's circuit.
Background technology
Chaos system has a very abundant dynamic behavior, and cai's circuit (chua ' s circuit) for the first time in chaos
Erecting bridge between theory and chaos circuit so that chaos system application is provided with engineering background, chaos system controlling, will lead to
The fields such as letter, mathematics, physics, biology have a wide range of applications.
Application No. 2008101292162, Publication No. CN 101295454A " a kind of non-inductor Chua circuit ", is right
Famous cai's circuit realizes with the circuit of another form, does not study the system equation of cai's circuit, and
And designed circuit can not promote the chaotic dynamics behavior of former cai's circuit.
Summary of the invention
It is an object of the invention to overcome problems of the prior art, it is provided that the Cai Shi that a kind of hysteresis function realizes
Circuit, it is adaptable to university's chaos education of science, experimental teaching and demonstration, scientific popularization experimental demonstration etc., can be widely applied to
In voice analog signal secret signalling.
The present invention realizes above-mentioned purpose, the technical scheme is that
A new chaos system is proposed on the basis of cai's circuit (chua ' s circuit) chaos system is carried out in-depth study
System, new accountant rule equation is as follows:
Wherein g (x) is hysteresis function, and expression formula is:
Comparison accompanying drawing 1, as x ＜-1, increases x, until 1, then increase, g (x) value is u from-u transition；As x ＞ 1, reduce x,
Until-1, then reduce, g (x) value is-u from u transition；As-1 ＜ x ＜ 1, g (x) value is constant.
And cai's circuit chaos system equation is as follows:
Wherein:
New accountant rule (a kind of hysteresis function realize cai's circuit) compared with cai's circuit chaos system, new system non-thread
Property item g (x) and f (x) different.
The cai's circuit that a kind of hysteresis function realizes, is characterized in that: by six operational amplifiers and 14 electricity
Resistance and three electric capacity are constituted, wherein: the first operational amplifier A1Inverting input and the 3rd resistance R3, the 8th resistance R8Connect,
First operational amplifier A1In-phase input end ground connection, the first operational amplifier A1Inverting input and outfan between be connected
First resistance R in parallel1With the first electric capacity C1, the first operational amplifier A1Outfan and the 9th resistance R9, the 13rd resistance R13
Connect, the first operational amplifier A1Outfan be X outfan；Second operational amplifier A2Inverting input and the 4th electricity
Resistance R4Connect, the second operational amplifier A2In-phase input end ground connection, the second operational amplifier A2Inverting input and outfan
Between connect parallel connection the second resistance R2With the second electric capacity C2, the second operational amplifier A2Outfan and the 5th resistance R5, the 7th
Resistance R7Connect, the second operational amplifier A2Outfan be Y outfan；3rd operational amplifier A3Inverting input with
5th resistance R5Connect, the 3rd operational amplifier A3In-phase input end ground connection, the 3rd operational amplifier A3Inverting input with
The 3rd electric capacity C is connected between outfan3, the 3rd operational amplifier A3Outfan and the 14th resistance R14Connect, the 3rd computing
Amplifier A3Outfan be Z outfan；Four-operational amplifier A4Inverting input and the 7th resistance R7Connect, the 4th
Operational amplifier A4In-phase input end ground connection, four-operational amplifier A4Inverting input and outfan between be connected the 6th
Resistance R6, four-operational amplifier A4Outfan and the 3rd resistance R3Connect；5th operational amplifier A5Inverting input with
9th resistance R9Connect, the 5th operational amplifier A5In-phase input end and outfan between be connected the tenth resistance R10, the 5th fortune
Calculate amplifier A5In-phase input end and the 11st resistance R11Connect, the 11st resistance R11Other end ground connection, the 5th computing is put
Big device A5Outfan and the 8th resistance R8Connect；6th operational amplifier A6Inverting input and the 13rd resistance R13, the tenth
Four resistance R14Connect, the 6th operational amplifier A6In-phase input end ground connection, the 6th operational amplifier A6Inverting input with
The 12nd resistance R is connected between outfan12, the 6th operational amplifier A6Outfan and the 4th resistance R4Connect.
Described first resistance R1, the second resistance R2, the 3rd resistance R3, the 5th resistance R5, the 13rd resistance R13With the 14th electricity
Resistance R14Replace with potentiometer, change the first resistance R1, the second resistance R2, the 3rd resistance R3, the 5th resistance R5, the 13rd resistance R13
With the 14th resistance R14Resistance can observe chaos circuit develop various curves.
The invention has the beneficial effects as follows: the present invention enriches cai's circuit chaos system, deepened people to chaos system
Understanding.Ordinary oscilloscope is phasor and the chaos differentiation song of the observable cai's circuit chaos system containing hysteresis function
Line, i.e. the oscillogram of each outfan of observable X, Y, Z, it is possible to observe X-Y, X-Z, Y-Z phasor, the present invention is applicable to university and mixes
Ignorant education of science, experimental teaching and demonstration, scientific popularization experimental demonstration etc., the method can be widely used in voice analog signal secrecy
In communication system.
Accompanying drawing illustrates:
Fig. 1 is the performance diagram of hysteresis function g (x) of the present invention；
Fig. 2 is the schematic diagram of the cai's circuit that hysteresis function of the present invention realizes；
Fig. 3 is the X outfan oscillogram of the cai's circuit that present invention hysteresis function realizes；
Fig. 4 is the Y outfan oscillogram of the cai's circuit that present invention hysteresis function realizes；
Fig. 5 is the Z outfan oscillogram of the cai's circuit that present invention hysteresis function realizes；
Fig. 6 is the X-Y outfan phasor of the cai's circuit that present invention hysteresis function realizes；
Fig. 7 is the X-Z outfan phasor of the cai's circuit that present invention hysteresis function realizes；
Fig. 8 is the Y-Z outfan phasor of the cai's circuit that present invention hysteresis function realizes.
Detailed description of the invention:
Below in conjunction with drawings and Examples, the invention will be further described.
Embodiment 1:
With reference to Fig. 2, by the cai's circuit realized with hysteresis function, it is characterized in that: by six operational amplifiers and 14 electricity
Resistance and three electric capacity are constituted, wherein: the first operational amplifier A1Inverting input and the 3rd resistance R3, the 8th resistance R8Connect,
First operational amplifier A1In-phase input end ground connection, the first operational amplifier A1Inverting input and outfan between be connected
First resistance R in parallel1With the first electric capacity C1, the first operational amplifier A1Outfan and the 9th resistance R9, the 13rd resistance R13
Connect, the first operational amplifier A1Outfan be X outfan；Second operational amplifier A2Inverting input and the 4th electricity
Resistance R4Connect, the second operational amplifier A2In-phase input end ground connection, the second operational amplifier A2Inverting input and outfan
Between connect parallel connection the second resistance R2With the second electric capacity C2, the second operational amplifier A2Outfan and the 5th resistance R5, the 7th
Resistance R7Connect, the second operational amplifier A2Outfan be Y outfan；3rd operational amplifier A3Inverting input with
5th resistance R5Connect, the 3rd operational amplifier A3In-phase input end ground connection, the 3rd operational amplifier A3Inverting input with
The 3rd electric capacity C is connected between outfan3, the 3rd operational amplifier A3Outfan and the 14th resistance R14Connect, the 3rd computing
Amplifier A3Outfan be Z outfan；Four-operational amplifier A4Inverting input and the 7th resistance R7Connect, the 4th
Operational amplifier A4In-phase input end ground connection, four-operational amplifier A4Inverting input and outfan between be connected the 6th
Resistance R6, four-operational amplifier A4Outfan and the 3rd resistance R3Connect；5th operational amplifier A5Inverting input with
9th resistance R9Connect, the 5th operational amplifier A5In-phase input end and outfan between be connected the tenth resistance R10, the 5th fortune
Calculate amplifier A5In-phase input end and the 11st resistance R11Connect, the 11st resistance R11Other end ground connection, the 5th computing is put
Big device A5Outfan and the 8th resistance R8Connect；6th operational amplifier A6Inverting input and the 13rd resistance R13, the tenth
Four resistance R14Connect, the 6th operational amplifier A6In-phase input end ground connection, the 6th operational amplifier A6Inverting input with
The 12nd resistance R is connected between outfan12, the 6th operational amplifier A6Outfan and the 4th resistance R4Connect.
Work as electric capacity: C1=C2=C3=100nF, resistance: R1=8K Ω, R2=10K Ω, R3= R4=10K Ω, R5=0.6K Ω, R6=
10K Ω, R7=1K Ω, R8=50K Ω, R9=1K Ω, R10=15K Ω, R11=2K Ω, R12=10K Ω, R13=10K Ω, R14=10K Ω,
When operational amplifier uses μ A741, X outfan, Y outfan, Z outfan in Fig. 2 are connected to oscilloscope signal input, can
To show the oscillogram of X, Y, Z outfan, as shown in Fig. 3, Fig. 4, Fig. 5, using oscillographic phasor mode, X-Y is defeated in observation
Go out to hold phasor, X-Z outfan phasor, Y-Z outfan phasor, as shown in Fig. 6, Fig. 7, Fig. 8, it was demonstrated that the present invention's is effective
Property.
Embodiment 2:
Described first resistance R1, the second resistance R2, the 3rd resistance R3, the 5th resistance R5, the 13rd resistance R13With the 14th resistance
R14Replace with potentiometer, change its resistance and can observe the various curves that this chaos circuit develops.
Claims (2)
1. the cai's circuit realized with hysteresis function, is characterized in that: by six operational amplifiers and 14 resistance
Constitute with three electric capacity, wherein: the first operational amplifier A1Inverting input and the 3rd resistance R3, the 8th resistance R8Connect, the
One operational amplifier A1In-phase input end ground connection, the first operational amplifier A1Inverting input and outfan between be connected also
First resistance R of connection1With the first electric capacity C1, the first operational amplifier A1Outfan and the 9th resistance R9, the 13rd resistance R13Even
Connect, the first operational amplifier A1Outfan be X outfan；Second operational amplifier A2Inverting input and the 4th resistance
R4Connect, the second operational amplifier A2In-phase input end ground connection, the second operational amplifier A2Inverting input and outfan it
Between connect parallel connection the second resistance R2With the second electric capacity C2, the second operational amplifier A2Outfan and the 5th resistance R5, the 7th electricity
Resistance R7Connect, the second operational amplifier A2Outfan be Y outfan；3rd operational amplifier A3Inverting input and
Five resistance R5Connect, the 3rd operational amplifier A3In-phase input end ground connection, the 3rd operational amplifier A3Inverting input with defeated
Go out and between end, connect the 3rd electric capacity C3, the 3rd operational amplifier A3Outfan and the 14th resistance R14Connecting, the 3rd computing is put
Big device A3Outfan be Z outfan；Four-operational amplifier A4Inverting input and the 7th resistance R7Connect, the 4th fortune
Calculate amplifier A4In-phase input end ground connection, four-operational amplifier A4Inverting input and outfan between be connected the 6th electricity
Resistance R6, four-operational amplifier A4Outfan and the 3rd resistance R3Connect；5th operational amplifier A5Inverting input and
Nine resistance R9Connect, the 5th operational amplifier A5In-phase input end and outfan between be connected the tenth resistance R10, the 5th computing
Amplifier A5In-phase input end and the 11st resistance R11Connect, the 11st resistance R11Other end ground connection, the 5th operation amplifier
Device A5Outfan and the 8th resistance R8Connect；6th operational amplifier A6Inverting input and the 13rd resistance R13, the 14th
Resistance R14Connect, the 6th operational amplifier A6In-phase input end ground connection, the 6th operational amplifier A6Inverting input with defeated
Go out and between end, connect the 12nd resistance R12, the 6th operational amplifier A6Outfan and the 4th resistance R4Connect.
The cai's circuit that a kind of hysteresis function the most according to claim 1 realizes, it is characterised in that: described first resistance
R1, the second resistance R2, the 3rd resistance R3, the 5th resistance R5, the 13rd resistance R13With the 14th resistance R14Replace with potentiometer, change
Become the first resistance R1, the second resistance R2, the 3rd resistance R3, the 5th resistance R5, the 13rd resistance R13With the 14th resistance R14Resistance
The various curves that chaos circuit develops can be observed.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610345238.7A CN105845004A (en) | 2016-05-24 | 2016-05-24 | Chua's circuit realized based on hysteresis function |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610345238.7A CN105845004A (en) | 2016-05-24 | 2016-05-24 | Chua's circuit realized based on hysteresis function |
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| CN105845004A true CN105845004A (en) | 2016-08-10 |
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| Application Number | Title | Priority Date | Filing Date |
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| CN201610345238.7A Pending CN105845004A (en) | 2016-05-24 | 2016-05-24 | Chua's circuit realized based on hysteresis function |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106992849A (en) * | 2017-05-10 | 2017-07-28 | 河南应用技术职业学院 | A kind of two-dimentional four scroll chaotic circuit |
| CN109167658A (en) * | 2018-10-31 | 2019-01-08 | 史林鑫 | A kind of three rank Hysteretic nonlinearity chaos circuits |
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| CN103441835A (en) * | 2013-08-30 | 2013-12-11 | 河南工业职业技术学院 | Device and method for chaotic encryption communication experiment |
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2016
- 2016-05-24 CN CN201610345238.7A patent/CN105845004A/en active Pending
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| CN202475445U (en) * | 2012-02-16 | 2012-10-03 | 滨州学院 | Multifunctional general chaotic circuit system |
| CN103441835A (en) * | 2013-08-30 | 2013-12-11 | 河南工业职业技术学院 | Device and method for chaotic encryption communication experiment |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106992849A (en) * | 2017-05-10 | 2017-07-28 | 河南应用技术职业学院 | A kind of two-dimentional four scroll chaotic circuit |
| CN106992849B (en) * | 2017-05-10 | 2023-04-18 | 河南应用技术职业学院 | Two-dimensional four-scroll chaotic circuit |
| CN109167658A (en) * | 2018-10-31 | 2019-01-08 | 史林鑫 | A kind of three rank Hysteretic nonlinearity chaos circuits |
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Application publication date: 20160810 |