CN105227159A

CN105227159A - A kind of spherical five quasi-periodic oscillation systems and circuit

Info

Publication number: CN105227159A
Application number: CN201510531228.8A
Authority: CN
Inventors: 韩敬伟
Original assignee: Individual
Current assignee: Individual
Priority date: 2015-08-26
Filing date: 2015-08-26
Publication date: 2016-01-06

Abstract

The present invention relates to a kind of non linear system, in particular to spherical five the quasi-periodic oscillation systems of one and circuit, more common oscillator is period oscillator at present, chaotic oscillator can produce periodic oscillation system under different parameters, also quasi-periodicity and chaotic oscillation system 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 spherical five quasi-periodic oscillation systems, increase the type of oscillator, for oscillator application in the many a kind of selections newly of engineering practice.

Description

A kind of spherical five quasi-periodic oscillation systems and circuit

Technical field

The present invention relates to a kind of non linear system, particularly a kind of five spherical quasi-periodic oscillation systems 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 five spherical quasi-periodic oscillation systems, 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 five spherical quasi-periodic oscillation systems and circuit, and the present invention adopts following technological means to realize goal of the invention:

1. spherical five quasi-periodic oscillation systems, is characterized in that, comprise the following steps:

(1) following non linear system is considered:

(\begin{matrix} \overset{\cdot}{x} \\ \overset{\cdot}{y} \\ \overset{\cdot}{z} \end{matrix}) = (\begin{matrix} f (x, y, z) \\ g (x, y, z) \\ h (x, y, z) \end{matrix}) + (\begin{matrix} C_{1} \\ C_{2} \\ C_{3} \end{matrix}) - - - i

C in formula ₁, C ₂, C ₃for constant;

(2) JacobianMatrix (Jacobian matrix) of i formula is:

J = (\begin{matrix} \frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} & \frac{\partial f}{\partial z} \\ \frac{\partial g}{\partial x} & \frac{\partial g}{\partial y} & \frac{\partial g}{\partial z} \\ \frac{\partial h}{\partial x} & \frac{\partial h}{\partial y} & \frac{\partial h}{\partial z} \end{matrix}) - - - i i

(3) when the Jacobian matrix in ii is:

J = (\begin{matrix} 0 & 0 & a \\ 0 & 0 & - 2 z \\ - a & z & y \end{matrix})

System i is turned into

\{\begin{matrix} \overset{\cdot}{x} = a z + C_{1} \\ \overset{\cdot}{y} = - z^{2} + C_{2} \\ \overset{\cdot}{z} = - a x + y z + C_{3} \end{matrix} - - - i i i

Work as a=10, C ₂=2, C ₁=C ₃when=0, system is a kind of spherical five quasi-periodic oscillation systems.

2, a kind of spherical five quasi-periodic oscillation circuit systems, it is characterized in that: according to the Mathematical Modeling iii constructing analog circuit of spherical five quasi-periodic oscillation systems, operational amplifier U1, operational amplifier U2 and resistance and electric capacity is utilized to form anti-phase adder and anti-phase fractional order integrator, multiplier U3 and multiplier U4 is utilized to realize multiplying, DC power 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 and multiplier U3, 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, connect the 1st pin of multiplier U3, 8th pin connects and exports x, connected with the 2nd pin of operational amplifier U2 by resistance R11, 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 13rd pin of operational amplifier U2 by resistance R4, 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-z, connect the 3rd pin of multiplier U4, 8th pin connects and exports z, connected with the 13rd pin of operational amplifier U1 by resistance R2, connected with the 6th pin of operational amplifier U2 by resistance R13, connect the 3rd pin of multiplier U3, connect the 1st pin of multiplier U4, 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 DC power supply V1, the other end is connected with the 2nd pin of operational amplifier U1 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 2nd pin by resistance R7, 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 R1, and the 8th pin meets VCC.

The invention has the beneficial effects as follows: propose a kind of five spherical quasi-periodic oscillation circuit systems, 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 in the present invention.

Fig. 7 is the circuit connection diagram of U2 and U4 in 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) following non linear system is considered:

(\begin{matrix} \overset{\cdot}{x} \\ \overset{\cdot}{y} \\ \overset{\cdot}{z} \end{matrix}) = (\begin{matrix} f (x, y, z) \\ g (x, y, z) \\ h (x, y, z) \end{matrix}) + (\begin{matrix} C_{1} \\ C_{2} \\ C_{3} \end{matrix}) - - - i

C in formula ₁, C ₂, C ₃for constant;

(2) JacobianMatrix (Jacobian matrix) of i formula is:

J = (\begin{matrix} \frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} & \frac{\partial f}{\partial z} \\ \frac{\partial g}{\partial x} & \frac{\partial g}{\partial y} & \frac{\partial g}{\partial z} \\ \frac{\partial h}{\partial x} & \frac{\partial h}{\partial y} & \frac{\partial h}{\partial z} \end{matrix}) - - - i i

(3) when the Jacobian matrix in ii is:

J = (\begin{matrix} 0 & 0 & a \\ 0 & 0 & - 2 z \\ - a & z & y \end{matrix})

System i is turned into

\{\begin{matrix} \overset{\cdot}{x} = a z + C_{1} \\ \overset{\cdot}{y} = - z^{2} + C_{2} \\ \overset{\cdot}{z} = - a x + y z + C_{3} \end{matrix} - - - i i i

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

(1) following non linear system is considered:

(\begin{matrix} \overset{\cdot}{x} \\ \overset{\cdot}{y} \\ \overset{\cdot}{z} \end{matrix}) = (\begin{matrix} f (x, y, z) \\ g (x, y, z) \\ h (x, y, z) \end{matrix}) + (\begin{matrix} C_{1} \\ C_{2} \\ C_{3} \end{matrix}) - - - i

C in formula ₁, C ₂, C ₃for constant;

(2) JacobianMatrix (Jacobian matrix) of i formula is:

J = (\begin{matrix} \frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} & \frac{\partial f}{\partial z} \\ \frac{\partial g}{\partial x} & \frac{\partial g}{\partial y} & \frac{\partial g}{\partial z} \\ \frac{\partial h}{\partial x} & \frac{\partial h}{\partial y} & \frac{\partial h}{\partial z} \end{matrix}) - - - i i

(3) when the Jacobian matrix in ii is:

J = (\begin{matrix} 0 & 0 & a \\ 0 & 0 & - 2 z \\ - a & z & y \end{matrix})

System i is turned into

\{\begin{matrix} \overset{\cdot}{x} = a z + C_{1} \\ \overset{\cdot}{y} = - z^{2} + C_{2} \\ \overset{\cdot}{z} = - a x + y z + C_{3} \end{matrix} - - - i i i

2. spherical five quasi-periodic oscillation circuit systems, it is characterized in that: according to the Mathematical Modeling iii constructing analog circuit of spherical five quasi-periodic oscillation systems, operational amplifier U1, operational amplifier U2 and resistance and electric capacity is utilized to form anti-phase adder and anti-phase fractional order integrator, multiplier U3 and multiplier U4 is utilized to realize multiplying, DC power 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;