CN105183964A

CN105183964A - Spherical five-item quasi-periodic oscillator and circuit

Info

Publication number: CN105183964A
Application number: CN201510534151.XA
Authority: CN
Inventors: 韩敬伟
Original assignee: Individual
Current assignee: Individual
Priority date: 2015-08-26
Filing date: 2015-08-26
Publication date: 2015-12-23

Abstract

The present invention relates to a non-linear system, and in particular, to a spherical five-item quasi-periodic oscillator and a circuit. Currently, a currently common oscillator is a period oscillator, and a chaotic oscillator can generate a periodic oscillation system and a quasi-periodic and chaotic oscillation system with different parameters, but a system that only generates a quasi-periodic oscillator is not yet found. The present invention proposes a five-item spherical quasi-periodic oscillation system, so that a type of the oscillator is increased, thereby providing a new selection for the oscillator applied to engineering practice.

Description

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

Technical field

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

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

(1) following nonlinear 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 (Jacobi 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 Jacobi matrix in ii is:

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

System i is turned into

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

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

2, a kind of spherical five quasi-periodic oscillation device circuit, it is characterized in that: according to the mathematical model iii constructing analog circuit of spherical five quasi-periodic oscillation devices, 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 and multiplier U4, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U1;

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 6th pin of operational amplifier U2 by resistance R13, connect the 3rd pin of multiplier U3, 8th pin connects and exports x, connected with the 2nd pin of operational amplifier U2 by resistance R11, connect the 1st 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 13rd pin of operational amplifier U2 by resistance R4, 1st pin meets output-x, connect the 1st pin of multiplier U4, 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, 8th pin connects and exports z, connected with the 13rd pin of operational amplifier U1 by resistance R2, 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 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 13rd pin by resistance R1, 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 U1 the 2nd pin by resistance R7, and the 8th pin meets VCC.

The invention has the beneficial effects as follows: propose a kind of five spherical quasi-periodic oscillation devices, 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 and U4 in the present invention.

Fig. 7 is the circuit connection diagram of U2 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 nonlinear 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 (Jacobi 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 Jacobi matrix in ii is:

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

System i is turned into

\{\begin{matrix} \overset{\cdot}{x} = a z + x y + C_{1} \\ \overset{\cdot}{y} = - x^{2} + C_{2} \\ \overset{\cdot}{z} = - a x + 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 nonlinear 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 (Jacobi 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 Jacobi matrix in ii is:

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

System i is turned into

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

2. spherical five quasi-periodic oscillation device circuit, it is characterized in that: according to the mathematical model iii constructing analog circuit of spherical five quasi-periodic oscillation devices, 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;