CN102930762A - Three-dimensional chaotic circuit - Google Patents

Three-dimensional chaotic circuit Download PDF

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Publication number
CN102930762A
CN102930762A CN2012104678880A CN201210467888A CN102930762A CN 102930762 A CN102930762 A CN 102930762A CN 2012104678880 A CN2012104678880 A CN 2012104678880A CN 201210467888 A CN201210467888 A CN 201210467888A CN 102930762 A CN102930762 A CN 102930762A
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operational amplifier
output terminal
resistance
inverting input
connect
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CN2012104678880A
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Inventor
何怡刚
吴先明
罗旗舞
于文新
郑剑
尹柏强
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Hunan University
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Hunan University
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Abstract

The invention discloses a three-dimensional chaotic circuit, which comprises two analog multipliers, eight operational amplifiers, a resistor and a capacitor. By adopting the three-dimensional chaotic circuit disclosed by the invention, not only X-oscillograph, Y-oscillograph and Z-oscillograph but also X-Y phase diagram, X-Z phase diagram and Y-X phase diagram can be observed on a common oscilloscope. With the use of the three-dimensional chaotic circuit, a Lorenz system is enriched, and understanding of people on a chaotic system is deepen; and the three-dimensional chaotic circuit is suitable for chaotic science, experimental teaching and demonstration, popularization of science, experiment demonstration, and the like in universities. By using the three-dimensional chaotic circuit, various oscillographs, phase diagrams and chaotic evolution curves can be displayed.

Description

A kind of three-dimensional chaos circuit
Technical field
The invention belongs to non-linear circuit, be specifically related to a kind of three-dimensional chaos circuit.
Background technology
Chaology is constantly changing people to many traditional view of real world.Chaos has wide practical use in the fields such as bioengineering, mechanics engineering, electronic engineering, chemical engineering, information engineering, computer engineering, applied mathematics and experimental physics.
Application number is 02158943.7, and publication number is CN1512463A " lorentz equation experiment instrument "; With application number be 200810145285.2, publication number is that CN101373563A " a kind of Lorentz chaos circuit " is that famous Lorentz chaotic system is realized with different circuit, the Lorentz chaotic system equation is not studied.And designed circuit do not have transplantability, changes a kind of chaos system and just is difficult to realize.
Summary of the invention
The technical problem to be solved in the present invention is, overcomes the defects that prior art exists, and provides a kind of working stability reliable three-dimensional chaos circuit.
The technical solution adopted for the present invention to solve the technical problems is:
A kind of three-dimensional chaos circuit is made of two analog multipliers, eight operational amplifiers and resistance and electric capacity, wherein the second operational amplifier U 2Inverting input and the 4th resistance R 4Connect the second operational amplifier U 2In-phase input end ground connection, the second operational amplifier U 2Inverting input and output terminal between be provided with the first capacitor C 1, the second operational amplifier U 2Output terminal is the X output terminal, the second operational amplifier U 2Output terminal connects the 5th resistance R 5The 5th operational amplifier U 5Inverting input and the tenth resistance R 10Connect the 5th operational amplifier U 5In-phase input end ground connection, the 5th operational amplifier U 5Be connected the second capacitor C between inverting input and the output terminal 2, the 5th operational amplifier U 5Output terminal is the Y output terminal; The 7th operational amplifier U 7Inverting input and the 14 resistance R 14Connect the 7th operational amplifier U 7In-phase input end ground connection, the 7th operational amplifier U 7Be connected the 3rd capacitor C between inverting input and the output terminal 3, the 7th operational amplifier U 7Output terminal is the Z output terminal, the 7th operational amplifier U 7Output terminal connects the 15 resistance R 15The 3rd operational amplifier U 3Inverting input and the 5th resistance R 5, the 3rd operational amplifier U 3In-phase input end ground connection, the 3rd operational amplifier U 3Be connected the 6th resistance R between inverting input and the output terminal 6, the 3rd operational amplifier U 3Output terminal is the NOTX output terminal; The 8th operational amplifier U 8Inverting input and the 15 resistance R 15Connect the 8th operational amplifier U 8In-phase input end ground connection, the 8th operational amplifier U 8Be connected the 16 resistance R between inverting input and the output terminal 16, the 8th operational amplifier U 8Output terminal is the NOTZ output terminal; The first operational amplifier U 1Inverting input and the first resistance R 1, the second resistance R 2Connect the first resistance R 1The other end is connected with the Y output terminal again, the second resistance R 2The other end is connected with NOTX again, the first operational amplifier U 1In-phase input end ground connection, the first operational amplifier U 1Be connected the 3rd resistance R between inverting input and the output terminal 3, the first operational amplifier U 1Output terminal and the 4th resistance R 4Connect; Four-operational amplifier U 4Inverting input and the 7th resistance R 7, the 8th resistance R 8Connect the 7th resistance R 7The other end is connected with the X output terminal again, four-operational amplifier U 4In-phase input end ground connection, four-operational amplifier U 4Be connected the 9th resistance R between inverting input and the output terminal 9, four-operational amplifier U 4Output terminal and the tenth resistance R 10Connect; The 6th operational amplifier U 6Inverting input and the 11 resistance R 11, the 12 resistance R 12Connect the 11 resistance R 11The other end is connected with NOTZ again, the 6th operational amplifier U 6In-phase input end ground connection, the 6th operational amplifier U 6Be connected the 13 resistance R between inverting input and the output terminal 13, the 6th operational amplifier U 6Output terminal and the 14 resistance R 14Connect; The first analog multiplier A 1Two input ends are connected with NOTX output terminal, Z output terminal respectively, the first analog multiplier A 1Output terminal and the 8th resistance R 8Connect; The second analog multiplier A 2Two input ends are connected with X output terminal, Y output terminal respectively, the second analog multiplier A 2Output terminal and the 12 resistance R 12Connect.
Described the 7th resistance R 7Available potentiometer replaces, and changes its resistance and can observe the various curves that this chaos develops.
The present invention is to the Lorenz(Lorentz) chaos system carries out having proposed on the deep Research foundation a new chaos system, and there are 6 items in this system, and wherein coefficient is 2 of 1 quadratic terms, and new chaos system equation is as follows:
Figure 1141DEST_PATH_IMAGE001
And Lorenz chaos system equation is as follows:
Figure 2012104678880100002DEST_PATH_IMAGE002
New chaos system is compared with the Lorenz system, and second differential expressions of new system reduces by 1 linear y item.
Beneficial effect of the present invention is: observable X on ordinary oscilloscope, Y, the oscillogram of Z, also observable X-Y, X-Z, Y-Z phasor.The present invention has enriched the Lorenz system, has deepened the understanding of people to chaos system.The present invention is applicable to university's chaos science, experimental teaching and demonstration, scientific popularization with experimental demonstration etc., by the present invention, can show that various waveforms, phasor and chaos develop curve.
Description of drawings
Fig. 1 is three-dimensional chaos circuit theory diagrams of the present invention;
Fig. 2 is the X output waveform figure of three-dimensional chaos circuit of the present invention;
Fig. 3 is the Y output waveform figure of three-dimensional chaos circuit of the present invention;
Fig. 4 is the Z output waveform figure of three-dimensional chaos circuit of the present invention;
Fig. 5 is the X-Y output phasor of three-dimensional chaos circuit of the present invention;
Fig. 6 is the X-Z output phasor of three-dimensional chaos circuit of the present invention;
Fig. 7 is the Y-Z output phasor of three-dimensional chaos circuit of the present invention.
Embodiment
The invention will be further described below in conjunction with drawings and Examples.
With reference to Fig. 1, the present embodiment is made of two analog multipliers, eight operational amplifiers and resistance and electric capacity, wherein the second operational amplifier U 2Inverting input and the 4th resistance R 4Connect the second operational amplifier U 2In-phase input end ground connection, the second operational amplifier U 2Inverting input and output terminal between be provided with the first capacitor C 1, the second operational amplifier U 2Output terminal is the X output terminal, the second operational amplifier U 2Output terminal connects the 5th resistance R 5The 5th operational amplifier U 5Inverting input and the tenth resistance R 10Connect the 5th operational amplifier U 5In-phase input end ground connection, the 5th operational amplifier U 5Be connected the second capacitor C between inverting input and the output terminal 2, the 5th operational amplifier U 5Output terminal is the Y output terminal; The 7th operational amplifier U 7Inverting input and the 14 resistance R 14Connect the 7th operational amplifier U 7In-phase input end ground connection, the 7th operational amplifier U 7Be connected the 3rd capacitor C between inverting input and the output terminal 3, the 7th operational amplifier U 7Output terminal is the Z output terminal, the 7th operational amplifier U 7Output terminal connects the 15 resistance R 15The 3rd operational amplifier U 3Inverting input and the 5th resistance R 5, the 3rd operational amplifier U 3In-phase input end ground connection, the 3rd operational amplifier U 3Be connected the 6th resistance R between inverting input and the output terminal 6, the 3rd operational amplifier U 3Output terminal is the NOTX output terminal; The 8th operational amplifier U 8Inverting input and the 15 resistance R 15Connect the 8th operational amplifier U 8In-phase input end ground connection, the 8th operational amplifier U 8Be connected the 16 resistance R between inverting input and the output terminal 16, the 8th operational amplifier U 8Output terminal is the NOTZ output terminal; The first operational amplifier U 1Inverting input and the first resistance R 1, the second resistance R 2Connect the first resistance R 1The other end is connected with the Y output terminal again, the second resistance R 2The other end is connected with NOTX again, the first operational amplifier U 1In-phase input end ground connection, the first operational amplifier U 1Be connected the 3rd resistance R between inverting input and the output terminal 3, the first operational amplifier U 1Output terminal and the 4th resistance R 4Connect; Four-operational amplifier U 4Inverting input and the 7th resistance R 7, the 8th resistance R 8Connect the 7th resistance R 7The other end is connected with the X output terminal again, four-operational amplifier U 4In-phase input end ground connection, four-operational amplifier U 4Be connected the 9th resistance R between inverting input and the output terminal 9, four-operational amplifier U 4Output terminal and the tenth resistance R 10Connect; The 6th operational amplifier U 6Inverting input and the 11 resistance R 11, the 12 resistance R 12Connect the 11 resistance R 11The other end is connected with NOTZ again, the 6th operational amplifier U 6In-phase input end ground connection, the 6th operational amplifier U 6Be connected the 13 resistance R between inverting input and the output terminal 13, the 6th operational amplifier U 6Output terminal and the 14 resistance R 14Connect; The first analog multiplier A 1Two input ends are connected with NOTX output terminal, Z output terminal respectively, the first analog multiplier A 1Output terminal and the 8th resistance R 8Connect; The second analog multiplier A 2Two input ends are connected with X output terminal, Y output terminal respectively, the second analog multiplier A 2Output terminal and the 12 resistance R 12Connect.
According to Fig. 1, make a single face PCB chaos hardware circuit.Single face PCB chaos circuit making flow process is as follows: (1) is carried out circuit board wiring to Fig. 1 and is printed on the sensitive film; (2) on the sensitization single sided board, the circuit film is exposed; (3) photographic plate after the exposure is developed; (4) to the rotten copper of the photographic plate after developing; (5) bore the component pins hole; (6) be welded and fixed element.The positive supply V of multiplier AD633, operational amplifier μ A741 wherein DD, negative supply V EE, the GND wiring time partial line is arranged at top layer, adopt wire jumper to connect.
Work as capacitor C 1=C 2=C 3=10nF, resistance R 4=R 8=R 10=R 12=R 14=10K Ω, R 3=R 9=R 13=18K Ω, R 7=20K Ω, R 1=R 2=R 5=R 6=R 15=R 16=30K Ω, R 11=180K Ω, operational amplifier uses μ A741, and when analog multiplier used AD633, the oscillogram of circuit output was seen Fig. 2, Fig. 3, Fig. 4, and the phasor of circuit output is seen Fig. 5, Fig. 6, Fig. 7, and embodiment 1 circuit has been realized validity of the present invention fully.
Embodiment 2:
The difference of the present embodiment and embodiment 1 is:
Described the 7th resistance R 7Replace with potentiometer, change its resistance and can observe the various curves that this chaos develops.

Claims (2)

1. a three-dimensional chaos circuit is characterized in that, is made of two analog multipliers, eight operational amplifiers and resistance and electric capacity, wherein the second operational amplifier U 2Inverting input and the 4th resistance R 4Connect the second operational amplifier U 2In-phase input end ground connection, the second operational amplifier U 2Inverting input and output terminal between be provided with the first capacitor C 1, the second operational amplifier U 2Output terminal is the X output terminal, the second operational amplifier U 2Output terminal connects the 5th resistance R 5The 5th operational amplifier U 5Inverting input and the tenth resistance R 10Connect the 5th operational amplifier U 5In-phase input end ground connection, the 5th operational amplifier U 5Be connected the second capacitor C between inverting input and the output terminal 2, the 5th operational amplifier U 5Output terminal is the Y output terminal; The 7th operational amplifier U 7Inverting input and the 14 resistance R 14Connect the 7th operational amplifier U 7In-phase input end ground connection, the 7th operational amplifier U 7Be connected the 3rd capacitor C between inverting input and the output terminal 3, the 7th operational amplifier U 7Output terminal is the Z output terminal, the 7th operational amplifier U 7Output terminal connects the 15 resistance R 15The 3rd operational amplifier U 3Inverting input and the 5th resistance R 5, the 3rd operational amplifier U 3In-phase input end ground connection, the 3rd operational amplifier U 3Be connected the 6th resistance R between inverting input and the output terminal 6, the 3rd operational amplifier U 3Output terminal is the NOTX output terminal; The 8th operational amplifier U 8Inverting input and the 15 resistance R 15Connect the 8th operational amplifier U 8In-phase input end ground connection, the 8th operational amplifier U 8Be connected the 16 resistance R between inverting input and the output terminal 16, the 8th operational amplifier U 8Output terminal is the NOTZ output terminal; The first operational amplifier U 1Inverting input and the first resistance R 1, the second resistance R 2Connect the first resistance R 1The other end is connected with the Y output terminal again, the second resistance R 2The other end is connected with NOTX again, the first operational amplifier U 1In-phase input end ground connection, the first operational amplifier U 1Be connected the 3rd resistance R between inverting input and the output terminal 3, the first operational amplifier U 1Output terminal and the 4th resistance R 4Connect; Four-operational amplifier U 4Inverting input and the 7th resistance R 7, the 8th resistance R 8Connect the 7th resistance R 7The other end is connected with the X output terminal again, four-operational amplifier U 4In-phase input end ground connection, four-operational amplifier U 4Be connected the 9th resistance R between inverting input and the output terminal 9, four-operational amplifier U 4Output terminal and the tenth resistance R 10Connect; The 6th operational amplifier U 6Inverting input and the 11 resistance R 11, the 12 resistance R 12Connect the 11 resistance R 11The other end is connected with NOTZ again, the 6th operational amplifier U 6In-phase input end ground connection, the 6th operational amplifier U 6Be connected the 13 resistance R between inverting input and the output terminal 13, the 6th operational amplifier U 6Output terminal and the 14 resistance R 14Connect; The first analog multiplier A 1Two input ends are connected with NOTX output terminal, Z output terminal respectively, the first analog multiplier A 1Output terminal and the 8th resistance R 8Connect; The second analog multiplier A 2Two input ends are connected with X output terminal, Y output terminal respectively, the second analog multiplier A 2Output terminal and the 12 resistance R 12Connect.
2. three-dimensional chaos circuit according to claim 1 is characterized in that, described the 7th resistance R 7Replace with potentiometer.
CN2012104678880A 2012-11-19 2012-11-19 Three-dimensional chaotic circuit Pending CN102930762A (en)

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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103152159A (en) * 2013-03-17 2013-06-12 王少夫 Three-dimensional chaotic system with only one balance point and device thereof
CN103188071A (en) * 2013-04-03 2013-07-03 王少夫 Three-dimensional chaotic system and device thereof
CN108183787A (en) * 2018-03-20 2018-06-19 西北师范大学 A kind of comprehensive chaos circuit
CN108833076A (en) * 2018-06-27 2018-11-16 沈阳建筑大学 A kind of 16 parameter three-dimensional chaotic circuits
CN110620647A (en) * 2019-10-14 2019-12-27 江苏理工学院 Three-dimensional chaotic secret communication circuit
CN114978120A (en) * 2022-04-18 2022-08-30 常州大学 Hyperbolic sine, hyperbolic cosine and chaotic circuit

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1512463A (en) * 2002-12-27 2004-07-14 北京师范大学 Lorentz equation experiment instrument
CN101373563A (en) * 2008-08-01 2009-02-25 张新国 Lorentz chaos circuit

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CN1512463A (en) * 2002-12-27 2004-07-14 北京师范大学 Lorentz equation experiment instrument
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Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103152159A (en) * 2013-03-17 2013-06-12 王少夫 Three-dimensional chaotic system with only one balance point and device thereof
CN103188071A (en) * 2013-04-03 2013-07-03 王少夫 Three-dimensional chaotic system and device thereof
CN108183787A (en) * 2018-03-20 2018-06-19 西北师范大学 A kind of comprehensive chaos circuit
CN108183787B (en) * 2018-03-20 2021-08-17 西北师范大学 Comprehensive chaotic circuit
CN108833076A (en) * 2018-06-27 2018-11-16 沈阳建筑大学 A kind of 16 parameter three-dimensional chaotic circuits
CN108833076B (en) * 2018-06-27 2020-12-25 沈阳建筑大学 Sixteen-parameter three-dimensional chaotic circuit
CN110620647A (en) * 2019-10-14 2019-12-27 江苏理工学院 Three-dimensional chaotic secret communication circuit
CN110620647B (en) * 2019-10-14 2023-03-07 江苏理工学院 Three-dimensional chaotic secret communication circuit
CN114978120A (en) * 2022-04-18 2022-08-30 常州大学 Hyperbolic sine, hyperbolic cosine and chaotic circuit
CN114978120B (en) * 2022-04-18 2023-09-22 常州大学 Hyperbolic sine, hyperbolic cosine and chaotic circuit

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Application publication date: 20130213