CN105205310A - Spherical quasi-periodic oscillation system and circuit - Google Patents
Spherical quasi-periodic oscillation system and circuit Download PDFInfo
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- CN105205310A CN105205310A CN201510532777.7A CN201510532777A CN105205310A CN 105205310 A CN105205310 A CN 105205310A CN 201510532777 A CN201510532777 A CN 201510532777A CN 105205310 A CN105205310 A CN 105205310A
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Abstract
The invention relates to a nonlinear system and particularly relates to a spherical quasi-periodic oscillation system and a circuit. Currently, relatively common oscillators are periodic oscillators, a chaotic oscillator is capable of generating a rectilinear oscillation system under the different parameters and generating quasi-periodic and chaotic oscillation systems, and a system capable of only generating a quasi-periodic oscillator has not been developed yet. The invention discloses a spherical quasi-periodic oscillator, so that the type of the oscillators is increased, and a new choice is provided for the application of the oscillators to the engineering practice.
Description
Technical field
The present invention relates to a kind of nonlinear system, particularly the spherical quasi-periodic oscillation system of one and circuit.
Background technology
More common oscillator is period oscillator at present, chaotic oscillator can produce period oscillator under different parameters, also quasi-periodicity and chaotic oscillator can be produced, but the system only producing quasi-periodic oscillation device is not also found, the present invention shows and proposes a kind of quasi-periodicity spherical oscillator, increase the type of oscillator, for oscillator application in the many a kind of selections newly of engineering practice.
Summary of the invention
The technical problem to be solved in the present invention is to provide a kind of spherical quasi-periodic oscillation system and circuit, and the present invention adopts following technological means to realize goal of the invention:
1. a spherical quasi-periodic oscillation system, is characterized in that, comprise the following steps:
(1) following nonlinear system is considered:
C in formula
1, C
2, C
3for constant;
(2) JacobianMatrix (Jacobi matrix) of i formula is:
(3) when the Jacobi matrix in ii is:
System i is turned into
Work as a=10, b=10, c=1, C
3=2, C
1=C
2when=0, system is spherical quasi-periodic oscillation system.
2, a kind of spherical quasi-periodic oscillation circuit system, it is characterized in that: according to the mathematical model iii constructing analog circuit of spherical quasi-periodic oscillation system, operational amplifier U1, operational amplifier U2 and resistance and electric capacity is utilized to form anti-phase totalizer and anti-phase fractional order integrator, multiplier U3 and multiplier U4 is utilized to realize multiplying, direct supply V1 is utilized to realize constant inflow, described operational amplifier U1, operational amplifier U2 adopt LF347N, and described multiplier U3 and multiplier U4 adopts AD633JN;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and multiplier U4, described operational amplifier U2 concatenation operation amplifier U1, multiplier U3 and multiplier U4, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2;
1st pin of described operational amplifier U1 is connected with the 6th pin by resistance R3, 2nd pin is connected with the 1st pin by resistance R5, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected with the 7th pin by electric capacity C2, 7th pin connects and exports y, connected with the 13rd pin of operational amplifier U1 by resistance R2, connected with the 6th pin of operational amplifier U2 by resistance R13, 8th pin connects and exports x, connected with the 2nd pin of operational amplifier U2 by resistance R11, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, 9th pin is connected with the 8th pin by electric capacity C1, 13rd pin is connected with the 14th pin by resistance R9, 14th pin is connected with 9 pins by resistance R10,
1st pin of described operational amplifier U2 is connected with the 2nd pin of operational amplifier U1 by resistance R4, connected with the 13rd pin of operational amplifier U1 by resistance R19, connect the 1st pin of multiplier U4, 1st pin meets output-x, 2nd pin is connected with the 1st pin by resistance R12, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected with the 7th pin by resistance R14, 7th pin meets output-y, connected with the 13rd pin of operational amplifier U2 by resistance R7, 8th pin connects and exports z, connect the 1st pin of multiplier U3, connected with the 2nd pin of operational amplifier U1 by resistance R17, 9th pin is connected with the 8th pin by electric capacity C3, 13rd pin completes is crossed resistance R15 and is connected with the 14th pin, 14th pin is connected with the 9th pin by resistance R16,
One end ground connection of described direct supply V1, the other end is connected with the 13rd pin of operational amplifier U2 by resistance R8;
The equal ground connection of 2nd, 4,6 pin of described multiplier U3, the 5th pin meets VEE, and the 7th pin connects operational amplifier U1 the 13rd pin by resistance R6, and the 8th pin meets VCC;
The equal ground connection of 2nd, 4,6 pin of described multiplier U4, the 5th pin meets VEE, and the 7th pin connects operational amplifier U2 the 13rd pin by resistance R18, and the 8th pin meets VCC.
The invention has the beneficial effects as follows: propose a kind of quasi-periodicity spherical oscillatory system and circuit, add type and the kind of oscillator, for oscillator application provides a kind of selection newly in engineering practice.
Accompanying drawing explanation
Fig. 1 is the 3-D view of the spherical oscillator that the present invention proposes.
Fig. 2 is the view of the x-z plane of the spherical oscillator that the present invention proposes.
Fig. 3 is the view of the y-z plane of the spherical oscillator that the present invention proposes.
Fig. 4 is the view of the x-y plane of the spherical oscillator that the present invention proposes.
Fig. 5 is circuit structure diagram of the present invention.
Fig. 6 is the circuit connection diagram of U1 and U3 of the present invention.
Fig. 7 is the circuit connection diagram of U2 and U4 of the present invention.
Embodiment
Below in conjunction with accompanying drawing and preferred embodiment, the present invention is further described in detail, see Fig. 1-Fig. 7.
1. a spherical quasi-periodic oscillation system, is characterized in that, comprise the following steps:
(1) following nonlinear system is considered:
C in formula
1, C
2, C
3for constant;
(2) JacobianMatrix (Jacobi matrix) of i formula is:
(3) when the Jacobi matrix in ii is:
System i is turned into
Work as a=10, b=10, c=1, C
3=2, C
1=C
2when=0, system is spherical quasi-periodic oscillation system.
2, a kind of spherical quasi-periodic oscillation circuit system, it is characterized in that: according to the mathematical model iii constructing analog circuit of spherical quasi-periodic oscillation system, operational amplifier U1, operational amplifier U2 and resistance and electric capacity is utilized to form anti-phase totalizer and anti-phase fractional order integrator, multiplier U3 and multiplier U4 is utilized to realize multiplying, direct supply V1 is utilized to realize constant inflow, described operational amplifier U1, operational amplifier U2 adopt LF347N, and described multiplier U3 and multiplier U4 adopts AD633JN;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and multiplier U4, described operational amplifier U2 concatenation operation amplifier U1, multiplier U3 and multiplier U4, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2;
1st pin of described operational amplifier U1 is connected with the 6th pin by resistance R3, 2nd pin is connected with the 1st pin by resistance R5, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected with the 7th pin by electric capacity C2, 7th pin connects and exports y, connected with the 13rd pin of operational amplifier U1 by resistance R2, connected with the 6th pin of operational amplifier U2 by resistance R13, 8th pin connects and exports x, connected with the 2nd pin of operational amplifier U2 by resistance R11, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, 9th pin is connected with the 8th pin by electric capacity C1, 13rd pin is connected with the 14th pin by resistance R9, 14th pin is connected with 9 pins by resistance R10,
1st pin of described operational amplifier U2 is connected with the 2nd pin of operational amplifier U1 by resistance R4, connected with the 13rd pin of operational amplifier U1 by resistance R19, connect the 1st pin of multiplier U4, 1st pin meets output-x, 2nd pin is connected with the 1st pin by resistance R12, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected with the 7th pin by resistance R14, 7th pin meets output-y, connected with the 13rd pin of operational amplifier U2 by resistance R7, 8th pin connects and exports z, connect the 1st pin of multiplier U3, connected with the 2nd pin of operational amplifier U1 by resistance R17, 9th pin is connected with the 8th pin by electric capacity C3, 13rd pin completes is crossed resistance R15 and is connected with the 14th pin, 14th pin is connected with the 9th pin by resistance R16,
One end ground connection of described direct supply V1, the other end is connected with the 13rd pin of operational amplifier U2 by resistance R8;
The equal ground connection of 2nd, 4,6 pin of described multiplier U3, the 5th pin meets VEE, and the 7th pin connects operational amplifier U1 the 13rd pin by resistance R6, and the 8th pin meets VCC;
The equal ground connection of 2nd, 4,6 pin of described multiplier U4, the 5th pin meets VEE, and the 7th pin connects operational amplifier U2 the 13rd pin by resistance R18, and the 8th pin meets VCC.
Certainly, above-mentioned explanation is not limitation of the present invention, and the present invention is also not limited only to above-mentioned citing, and the change that those skilled in the art make in essential scope of the present invention, remodeling, interpolation or replacement, also belong to protection scope of the present invention.
Claims (2)
1. a spherical quasi-periodic oscillation system, is characterized in that, comprise the following steps:
(1) following nonlinear system is considered:
C in formula
1, C
2, C
3for constant;
(2) JacobianMatrix (Jacobi matrix) of i formula is:
(3) when the Jacobi matrix in ii is:
System i is turned into
Work as a=10, b=10, c=1, C
3=2, C
1=C
2when=0, system is spherical quasi-periodic oscillation system.
2. a spherical quasi-periodic oscillation circuit system, it is characterized in that: according to the mathematical model iii constructing analog circuit of spherical quasi-periodic oscillation system, operational amplifier U1, operational amplifier U2 and resistance and electric capacity is utilized to form anti-phase totalizer and anti-phase fractional order integrator, multiplier U3 and multiplier U4 is utilized to realize multiplying, direct supply V1 is utilized to realize constant inflow, described operational amplifier U1, operational amplifier U2 adopt LF347N, and described multiplier U3 and multiplier U4 adopts AD633JN;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3 and multiplier U4, described operational amplifier U2 concatenation operation amplifier U1, multiplier U3 and multiplier U4, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2;
1st pin of described operational amplifier U1 is connected with the 6th pin by resistance R3, 2nd pin is connected with the 1st pin by resistance R5, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected with the 7th pin by electric capacity C2, 7th pin connects and exports y, connected with the 13rd pin of operational amplifier U1 by resistance R2, connected with the 6th pin of operational amplifier U2 by resistance R13, 8th pin connects and exports x, connected with the 2nd pin of operational amplifier U2 by resistance R11, connect the 3rd pin of multiplier U3, connect the 3rd pin of multiplier U4, 9th pin is connected with the 8th pin by electric capacity C1, 13rd pin is connected with the 14th pin by resistance R9, 14th pin is connected with 9 pins by resistance R10,
1st pin of described operational amplifier U2 is connected with the 2nd pin of operational amplifier U1 by resistance R4, connected with the 13rd pin of operational amplifier U1 by resistance R19, connect the 1st pin of multiplier U4, 1st pin meets output-x, 2nd pin is connected with the 1st pin by resistance R12, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, 6th pin is connected with the 7th pin by resistance R14, 7th pin meets output-y, connected with the 13rd pin of operational amplifier U2 by resistance R7, 8th pin connects and exports z, connect the 1st pin of multiplier U3, connected with the 2nd pin of operational amplifier U1 by resistance R17, 9th pin is connected with the 8th pin by electric capacity C3, 13rd pin completes is crossed resistance R15 and is connected with the 14th pin, 14th pin is connected with the 9th pin by resistance R16,
One end ground connection of described direct supply V1, the other end is connected with the 13rd pin of operational amplifier U2 by resistance R8;
The equal ground connection of 2nd, 4,6 pin of described multiplier U3, the 5th pin meets VEE, and the 7th pin connects operational amplifier U1 the 13rd pin by resistance R6, and the 8th pin meets VCC;
The equal ground connection of 2nd, 4,6 pin of described multiplier U4, the 5th pin meets VEE, and the 7th pin connects operational amplifier U2 the 13rd pin by resistance R18, and the 8th pin meets VCC.
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Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN104202143A (en) * | 2014-08-31 | 2014-12-10 | 王春梅 | Four-dimensional balance point-free hyperchaotic system based on five-simplest chaotic system, and analogue circuit |
CN104539414A (en) * | 2015-01-04 | 2015-04-22 | 南开大学 | Simplest five-item chaotic system and circuit implementation method thereof |
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2015
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Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN104202143A (en) * | 2014-08-31 | 2014-12-10 | 王春梅 | Four-dimensional balance point-free hyperchaotic system based on five-simplest chaotic system, and analogue circuit |
CN104539414A (en) * | 2015-01-04 | 2015-04-22 | 南开大学 | Simplest five-item chaotic system and circuit implementation method thereof |
Non-Patent Citations (1)
Title |
---|
SUN CHANG-CHUN ET AL: "Generation of a novel spherical chaotic attractor from a new three-dimensional system", 《CHINESE PHYSICS B》 * |
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Application publication date: 20151230 |