CN103856317A - Method and circuit for switching classic Lorenz type chaotic system with different fractional orders - Google Patents

Abstract

The invention provides a method and circuit for switching a classic Lorenz type chaotic system provided with different fractional orders. An operational amplifier U1, an operational amplifier U2, a resistor and a capacitor are utilized for forming a reverse-phase summator and a fractional order reverse-phase integrator with different orders. A multiplying unit U3 and a multiplying unit U4 are utilized for achieving multiplication. An analog switch U5 is utilized for achieving selecting output of an analog signal. The type of the operational amplifier U1 and the type of the operational amplifier U2 are LF347D, the type of the multiplying unit U3 and the type of the multiplying unit U4 are AD633JN, and the type of the analog switch U5 is ADG888. The operational amplifier U1 is connected with the multiplying unit U3, the multiplying unit U4 and the analog switch U5, the operational amplifier U2 is connected with the multiplying unit U3 and the analog switch U5, the multiplying unit U3 is connected with the operational amplifier U1, the multiplying unit U4 is connected with the operational amplifier U2, and the analog switch U5 is connected with the operational amplifier U1 and the operational amplifier U2. The new method and circuit for switching the novel chaotic system are put forward, and a new idea is provided for increasing of the types of chaotic system switching and application to engineering practice of the chaotic system.

Description

Classical Lorenz type chaos switched system method and circuit that a kind of fractional-order is different

Technical field

The present invention relates to a chaos system and circuit and realize, particularly different classical Lorenz type chaos switched system method and the circuit of a kind of fractional-order.

Background technology

At present, the method of the switching chaos system that oneself has and main circuit to comprise different linear terms in chaos system or nonlinear terms between switching, and fractional order form based on these 2 kinds of switch modes, changing method and circuit about the chaotic systems with fractional order of different orders are not also suggested, the present invention proposes a kind of fractional-order different classical Lorenz type chaos switched system method and circuit, the present invention proposes New-type switching method and the circuit of a novel chaos system, the type that this switches increase chaos system and this chaos system are applied to engineering practice provides a kind of new approaches.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of fractional-order different classical Lorenz type chaos switched system method and circuit, and the present invention adopts following technological means to realize goal of the invention:

1, the different classical Lorenz type chaos switched system method of fractional-order, is characterized in that being, comprises the following steps:

(1) equation of Lorenz type chaos system i is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(y-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,i,a=20,b=14,c=10.6,h=2.8$

The equation of (2) 0.9 rank Lorenz type chaos system ii is:

$\left\{\begin{array}{c}{d}^{0.9}x/{\mathrm{dt}}^{0.9}=a(y-x)\\ d^{0.9}y/{\mathrm{dt}}^{0.9}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{0.9}z/{\mathrm{dt}}^{0.9}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,\mathrm{ii},a=20,b=14,c=10.6,h=2.8$

The equation of (3) 0.1 rank Lorenz type chaos system iii is:

$\left\{\begin{array}{c}{d}^{0.1}x/{\mathrm{dt}}^{0.1}=a(y-x)\\ d^{0.1}y/{\mathrm{dt}}^{0.1}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{0.1}z/{\mathrm{dt}}^{0.1}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,\mathrm{iii},a=20,b=14,c=10.6,h=2.8$

(4) structure switching function q=f (x), wherein the expression formula iv of f (x) is:

$q=f\left(x\right)=\left\{\begin{array}{cc}0.9& x>0\\ 0.1& x\≤0\end{array}\right.,\mathrm{iv}$

(5) constructing the different Lorenz type chaos switched system v of a kind of fractional-order by ii, iii and iv is:

$\left\{\begin{array}{c}{d}^{q}x/{\mathrm{dt}}^q=a(y-x)\\ d^{q}y/{\mathrm{dt}}^q=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{q}z/{\mathrm{dt}}^q=\mathrm{xy}-\mathrm{hz}\end{array}\right.,a=20,b=14,c=10.6,h=2.8,q=f\left(x\right)=\left\{\begin{array}{cc}0.9& x>0\\ 0.1& x\≤0\end{array}\right.,v$

(6) the Lorenz type chaos switched system v constructing analog Circuits System different according to fractional-order, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity form the fractional order inverting integrator of anti-phase adder and different orders, utilize multiplier U3 and multiplier U4 to realize multiplying, utilize analog switch U5 to realize the selection output of analog signal, described operational amplifier U1 and operational amplifier U2 adopt LF347D, described multiplier U3 and multiplier U4 adopt AD633JN, described analog switch U5 adopts ADG888, described operational amplifier U1 connects multiplier U3, multiplier U4 and analog switch U5, described operational amplifier U2 connects multiplier U3 and analog switch U5, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described analog switch U5 concatenation operation amplifier U1 and operational amplifier U2,

The 1st pin of described operational amplifier U1 joins by resistance R 3 and the 2nd pin of operational amplifier U1, join by resistance R 8 and the 6th pin of operational amplifier U1, the 3rd of operational amplifier U1, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin of operational amplifier U1 is in parallel by resistance R y11 and capacitor C y11's, connecting resistance Ry12 is in parallel with capacitor C y12's, again after connecting resistance Ry13 and capacitor C y13 in parallel, connect again the 7th pin of analog switch U5, in parallel by resistance R y21 and capacitor C y21, connecting resistance Ry22 is in parallel with capacitor C y22's, again after connecting resistance Ry23 and capacitor C y23 in parallel, connect again the 5th pin of analog switch U5, the 7th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 2, connect the 6th pin of operational amplifier U1 by resistance R 4, connect the 3rd pin of multiplier U4, the 8th pin of operational amplifier U1 connects the 2nd pin of operational amplifier U1 by resistance R 5, connect the 9th pin of operational amplifier U1 by resistance R 6, connect the 2nd pin of operational amplifier U2, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, the 9th pin of operational amplifier U1 is in parallel by resistance R x11 and capacitor C x11's, connecting resistance Rx12 is in parallel with capacitor C x12's, again after connecting resistance Rx13 and capacitor C x13 in parallel, connect again the 2nd pin of analog switch U5, in parallel by resistance R x21 and capacitor C x21, connecting resistance Rx22 is in parallel with capacitor C x22's, again after connecting resistance Rx23 and capacitor C x23 in parallel, connect again the 4th pin of analog switch U5, the 14th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 1, connect the 9th pin of operational amplifier U1 by resistance R 7,

The 6th of described operational amplifier U2, 7 pins are unsettled, the 3rd of described operational amplifier U2, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 1st pin of operational amplifier U2 is by the series connection ground connection of resistance R 14 and R15, meet the 8th of analog switch U5 by R14, 9 pins, the 8th pin of operational amplifier U2 connects the 9th pin of operational amplifier U2 by resistance R 12, connect the 3rd pin of multiplier U3, the 9th pin of operational amplifier U2 is in parallel by resistance R z11 and capacitor C z11's, connecting resistance Rz12 is in parallel with capacitor C z12's, again after connecting resistance Rz13 and capacitor C z13 in parallel, connect again the 10th pin of analog switch U5, in parallel by resistance R z21 and capacitor C z21, connecting resistance Rz22 is in parallel with capacitor C z22's, again after connecting resistance Rz23 and capacitor C z23 in parallel, connect again the 12nd pin of analog switch U5, the 14th pin of operational amplifier U2 connects the 13rd pin of operational amplifier U2 by resistance R 11, connect the 9th pin of operational amplifier U2 by resistance R 13,

The 1st pin of described multiplier U3 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 8th pin of operational amplifier U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 6th pin of operational amplifier U1 by resistance R 9, the 8th pin meets VCC;

The 1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 7th pin of operational amplifier U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance R 10, the 8th pin meets VCC;

The 1st pin of described analog switch U5 meets VCC, the 16th pin ground connection, and the 13rd, 14,15 pins are unsettled, and the 3rd pin connects the 8th pin of operational amplifier U1, and the 6th pin connects the 7th pin of operational amplifier U1, and the 11st pin connects the 8th pin of operational amplifier U2.

2, the Lorenz type chaos switched system circuit that a kind of fractional-order is different, it is characterized in that being, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity form the fractional order inverting integrator of anti-phase adder and different orders, utilize multiplier U3 and multiplier U4 to realize multiplying, utilize analog switch U5 to realize the selection output of analog signal, described operational amplifier U1 and operational amplifier U2 adopt LF347D, described multiplier U3 and multiplier U4 adopt AD633JN, described analog switch U5 adopts ADG888, described operational amplifier U1 connects multiplier U3, multiplier U4 and analog switch U5, described operational amplifier U2 connects multiplier U3 and analog switch U5, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described analog switch U5 concatenation operation amplifier U1 and operational amplifier U2,

The 1st pin of described operational amplifier U1 joins by resistance R 3 and the 2nd pin of operational amplifier U1, join by resistance R 8 and the 6th pin of operational amplifier U1, the 3rd of operational amplifier U1, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin of operational amplifier U1 is in parallel by resistance R y11 and capacitor C y11's, connecting resistance Ry12 is in parallel with capacitor C y12's, again after connecting resistance Ry13 and capacitor C y13 in parallel, connect again the 7th pin of analog switch U5, in parallel by resistance R y21 and capacitor C y21, connecting resistance Ry22 is in parallel with capacitor C y22's, again after connecting resistance Ry23 and capacitor C y23 in parallel, connect again the 5th pin of analog switch U5, the 7th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 2, connect the 6th pin of operational amplifier U1 by resistance R 4, connect the 3rd pin of multiplier U4, the 8th pin of operational amplifier U1 connects the 2nd pin of operational amplifier U1 by resistance R 5, connect the 9th pin of operational amplifier U1 by resistance R 6, connect the 2nd pin of operational amplifier U2, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, the 9th pin of operational amplifier U1 is in parallel by resistance R x11 and capacitor C x11's, connecting resistance Rx12 is in parallel with capacitor C x12's, again after connecting resistance Rx13 and capacitor C x13 in parallel, connect again the 2nd pin of analog switch U5, in parallel by resistance R x21 and capacitor C x21, connecting resistance Rx22 is in parallel with capacitor C x22's, again after connecting resistance Rx23 and capacitor C x23 in parallel, connect again the 4th pin of analog switch U5, the 14th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 1, connect the 9th pin of operational amplifier U1 by resistance R 7,

The 6th of described operational amplifier U2, 7 pins are unsettled, the 3rd of described operational amplifier U2, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 1st pin of operational amplifier U2 is by the series connection ground connection of resistance R 14 and R15, meet the 8th of analog switch U5 by R14, 9 pins, the 8th pin of operational amplifier U2 connects the 9th pin of operational amplifier U2 by resistance R 12, connect the 3rd pin of multiplier U3, the 9th pin of operational amplifier U2 is in parallel by resistance R z11 and capacitor C z11's, connecting resistance Rz12 is in parallel with capacitor C z12's, again after connecting resistance Rz13 and capacitor C z13 in parallel, connect again the 10th pin of analog switch U5, in parallel by resistance R z21 and capacitor C z21, connecting resistance Rz22 is in parallel with capacitor C z22's, again after connecting resistance Rz23 and capacitor C z23 in parallel, connect again the 12nd pin of analog switch U5, the 14th pin of operational amplifier U2 connects the 13rd pin of operational amplifier U2 by resistance R 11, connect the 9th pin of operational amplifier U2 by resistance R 13,

The 1st pin of described multiplier U3 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 8th pin of operational amplifier U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 6th pin of operational amplifier U1 by resistance R 9, the 8th pin meets VCC;

The 1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 7th pin of operational amplifier U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance R 10, the 8th pin meets VCC;

The 1st pin of described analog switch U5 meets VCC, the 16th pin ground connection, and the 13rd, 14,15 pins are unsettled, and the 3rd pin connects the 8th pin of operational amplifier U1, and the 6th pin connects the 7th pin of operational amplifier U1, and the 11st pin connects the 8th pin of operational amplifier U2.

The invention has the beneficial effects as follows: proposed New-type switching method and the circuit of a novel chaos system, the type that this switches increase chaos system and this chaos system are applied to engineering practice provides a kind of new approaches.

Accompanying drawing explanation

Fig. 1 is the circuit connection structure schematic diagram of the preferred embodiment of the present invention.

Fig. 2 and Fig. 3 are the actual connection layout of circuit of the present invention.

embodiment

Below in conjunction with accompanying drawing and preferred embodiment, the present invention is further described in detail, referring to Fig. 1-Fig. 2.

1, the different classical Lorenz type chaos switched system method of fractional-order, is characterized in that being, comprises the following steps:

(1) equation of Lorenz type chaos system i is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(y-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,i,a=20,b=14,c=10.6,h=2.8$

The equation of (2) 0.9 rank Lorenz type chaos system ii is:

$\left\{\begin{array}{c}{d}^{0.9}x/{\mathrm{dt}}^{0.9}=a(y-x)\\ d^{0.9}y/{\mathrm{dt}}^{0.9}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{0.9}z/{\mathrm{dt}}^{0.9}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,\mathrm{ii},a=20,b=14,c=10.6,h=2.8$

The equation of (3) 0.1 rank Lorenz type chaos system iii is:

$\left\{\begin{array}{c}{d}^{0.1}x/{\mathrm{dt}}^{0.1}=a(y-x)\\ d^{0.1}y/{\mathrm{dt}}^{0.1}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{0.1}z/{\mathrm{dt}}^{0.1}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,\mathrm{iii},a=20,b=14,c=10.6,h=2.8$

(4) structure switching function q=f (x), wherein the expression formula iv of f (x) is:

$q=f\left(x\right)=\left\{\begin{array}{cc}0.9& x>0\\ 0.1& x\≤0\end{array}\right.,\mathrm{iv}$

(5) constructing the different Lorenz type chaos switched system v of a kind of fractional-order by ii, iii and iv is:

$\left\{\begin{array}{c}{d}^{q}x/{\mathrm{dt}}^q=a(y-x)\\ d^{q}y/{\mathrm{dt}}^q=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{q}z/{\mathrm{dt}}^q=\mathrm{xy}-\mathrm{hz}\end{array}\right.,a=20,b=14,c=10.6,h=2.8,q=f\left(x\right)=\left\{\begin{array}{cc}0.9& x>0\\ 0.1& x\≤0\end{array}\right.,v$

(6) the Lorenz type chaos switched system v constructing analog Circuits System different according to fractional-order, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity form the fractional order inverting integrator of anti-phase adder and different orders, utilize multiplier U3 and multiplier U4 to realize multiplying, utilize analog switch U5 to realize the selection output of analog signal, described operational amplifier U1 and operational amplifier U2 adopt LF347D, described multiplier U3 and multiplier U4 adopt AD633JN, described analog switch U5 adopts ADG888, described operational amplifier U1 connects multiplier U3, multiplier U4 and analog switch U5, described operational amplifier U2 connects multiplier U3 and analog switch U5, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described analog switch U5 concatenation operation amplifier U1 and operational amplifier U2,

The 1st pin of described operational amplifier U1 joins by resistance R 3 and the 2nd pin of operational amplifier U1, join by resistance R 8 and the 6th pin of operational amplifier U1, the 3rd of operational amplifier U1, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin of operational amplifier U1 is in parallel by resistance R y11 and capacitor C y11's, connecting resistance Ry12 is in parallel with capacitor C y12's, again after connecting resistance Ry13 and capacitor C y13 in parallel, connect again the 7th pin of analog switch U5, in parallel by resistance R y21 and capacitor C y21, connecting resistance Ry22 is in parallel with capacitor C y22's, again after connecting resistance Ry23 and capacitor C y23 in parallel, connect again the 5th pin of analog switch U5, the 7th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 2, connect the 6th pin of operational amplifier U1 by resistance R 4, connect the 3rd pin of multiplier U4, the 8th pin of operational amplifier U1 connects the 2nd pin of operational amplifier U1 by resistance R 5, connect the 9th pin of operational amplifier U1 by resistance R 6, connect the 2nd pin of operational amplifier U2, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, the 9th pin of operational amplifier U1 is in parallel by resistance R x11 and capacitor C x11's, connecting resistance Rx12 is in parallel with capacitor C x12's, again after connecting resistance Rx13 and capacitor C x13 in parallel, connect again the 2nd pin of analog switch U5, in parallel by resistance R x21 and capacitor C x21, connecting resistance Rx22 is in parallel with capacitor C x22's, again after connecting resistance Rx23 and capacitor C x23 in parallel, connect again the 4th pin of analog switch U5, the 14th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 1, connect the 9th pin of operational amplifier U1 by resistance R 7,

The 6th of described operational amplifier U2, 7 pins are unsettled, the 3rd of described operational amplifier U2, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 1st pin of operational amplifier U2 is by the series connection ground connection of resistance R 14 and R15, meet the 8th of analog switch U5 by R14, 9 pins, the 8th pin of operational amplifier U2 connects the 9th pin of operational amplifier U2 by resistance R 12, connect the 3rd pin of multiplier U3, the 9th pin of operational amplifier U2 is in parallel by resistance R z11 and capacitor C z11's, connecting resistance Rz12 is in parallel with capacitor C z12's, again after connecting resistance Rz13 and capacitor C z13 in parallel, connect again the 10th pin of analog switch U5, in parallel by resistance R z21 and capacitor C z21, connecting resistance Rz22 is in parallel with capacitor C z22's, again after connecting resistance Rz23 and capacitor C z23 in parallel, connect again the 12nd pin of analog switch U5, the 14th pin of operational amplifier U2 connects the 13rd pin of operational amplifier U2 by resistance R 11, connect the 9th pin of operational amplifier U2 by resistance R 13,

The 1st pin of described multiplier U3 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 8th pin of operational amplifier U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 6th pin of operational amplifier U1 by resistance R 9, the 8th pin meets VCC;

The 1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 7th pin of operational amplifier U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance R 10, the 8th pin meets VCC;

The 1st pin of described analog switch U5 meets VCC, the 16th pin ground connection, and the 13rd, 14,15 pins are unsettled, and the 3rd pin connects the 8th pin of operational amplifier U1, and the 6th pin connects the 7th pin of operational amplifier U1, and the 11st pin connects the 8th pin of operational amplifier U2.

2, the Lorenz type chaos switched system circuit that a kind of fractional-order is different, it is characterized in that being, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity form the fractional order inverting integrator of anti-phase adder and different orders, utilize multiplier U3 and multiplier U4 to realize multiplying, utilize analog switch U5 to realize the selection output of analog signal, described operational amplifier U1 and operational amplifier U2 adopt LF347D, described multiplier U3 and multiplier U4 adopt AD633JN, described analog switch U5 adopts ADG888, described operational amplifier U1 connects multiplier U3, multiplier U4 and analog switch U5, described operational amplifier U2 connects multiplier U3 and analog switch U5, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described analog switch U5 concatenation operation amplifier U1 and operational amplifier U2,

The 1st pin of described operational amplifier U1 joins by resistance R 3 and the 2nd pin of operational amplifier U1, join by resistance R 8 and the 6th pin of operational amplifier U1, the 3rd of operational amplifier U1, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin of operational amplifier U1 is in parallel by resistance R y11 and capacitor C y11's, connecting resistance Ry12 is in parallel with capacitor C y12's, again after connecting resistance Ry13 and capacitor C y13 in parallel, connect again the 7th pin of analog switch U5, in parallel by resistance R y21 and capacitor C y21, connecting resistance Ry22 is in parallel with capacitor C y22's, again after connecting resistance Ry23 and capacitor C y23 in parallel, connect again the 5th pin of analog switch U5, the 7th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 2, connect the 6th pin of operational amplifier U1 by resistance R 4, connect the 3rd pin of multiplier U4, the 8th pin of operational amplifier U1 connects the 2nd pin of operational amplifier U1 by resistance R 5, connect the 9th pin of operational amplifier U1 by resistance R 6, connect the 2nd pin of operational amplifier U2, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, the 9th pin of operational amplifier U1 is in parallel by resistance R x11 and capacitor C x11's, connecting resistance Rx12 is in parallel with capacitor C x12's, again after connecting resistance Rx13 and capacitor C x13 in parallel, connect again the 2nd pin of analog switch U5, in parallel by resistance R x21 and capacitor C x21, connecting resistance Rx22 is in parallel with capacitor C x22's, again after connecting resistance Rx23 and capacitor C x23 in parallel, connect again the 4th pin of analog switch U5, the 14th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 1, connect the 9th pin of operational amplifier U1 by resistance R 7,

The 6th of described operational amplifier U2, 7 pins are unsettled, the 3rd of described operational amplifier U2, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 1st pin of operational amplifier U2 is by the series connection ground connection of resistance R 14 and R15, meet the 8th of analog switch U5 by R14, 9 pins, the 8th pin of operational amplifier U2 connects the 9th pin of operational amplifier U2 by resistance R 12, connect the 3rd pin of multiplier U3, the 9th pin of operational amplifier U2 is in parallel by resistance R z11 and capacitor C z11's, connecting resistance Rz12 is in parallel with capacitor C z12's, again after connecting resistance Rz13 and capacitor C z13 in parallel, connect again the 10th pin of analog switch U5, in parallel by resistance R z21 and capacitor C z21, connecting resistance Rz22 is in parallel with capacitor C z22's, again after connecting resistance Rz23 and capacitor C z23 in parallel, connect again the 12nd pin of analog switch U5, the 14th pin of operational amplifier U2 connects the 13rd pin of operational amplifier U2 by resistance R 11, connect the 9th pin of operational amplifier U2 by resistance R 13,

The 1st pin of described multiplier U3 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 8th pin of operational amplifier U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 6th pin of operational amplifier U1 by resistance R 9, the 8th pin meets VCC;

The 1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 7th pin of operational amplifier U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance R 10, the 8th pin meets VCC;

The 1st pin of described analog switch U5 meets VCC, the 16th pin ground connection, and the 13rd, 14,15 pins are unsettled, and the 3rd pin connects the 8th pin of operational amplifier U1, and the 6th pin connects the 7th pin of operational amplifier U1, and the 11st pin connects the 8th pin of operational amplifier U2.

Resistance R 1=R7=R3=R8=R11=R13=10k Ω in circuit, R2=R6=5k Ω, R4=9.4k Ω, R5=7.14k Ω, R9=R10=1k Ω, R12=35.7k Ω, R14=100k Ω, R15=80k Ω, Rx11=Ry11=Rz11=62.84M Ω, Rx12=Ry12=Rz12=250k Ω, Rx13=Ry13=Rz13=2.5k Ω, Rx21=Ry21=Rz21=0.636M Ω, Rx22=Ry22=Rz22=0.3815M Ω, Rx23=Ry23=Rz23=0.5672M Ω, Cx11=Cy11=Cz11=1.2 μ F, Cx12=Cy12=Cz13=1.8 μ F, Cx13=Cy13=Cz13=1.1 μ F, Cx21=Cy21=Cz21=15.75 μ F, Cx22=Cy22=Cz22=0.1575 μ F, Cx23=Cy23=Cz23=633.5nF.

Certainly, above-mentioned explanation is not limitation of the present invention, and the present invention is also not limited only to above-mentioned giving an example, and variation, remodeling, interpolation or replacement that those skilled in the art make in essential scope of the present invention, also belong to protection scope of the present invention.

Claims (2)

1. the different classical Lorenz type chaos switched system method of fractional-order, is characterized in that being, comprises the following steps:

(1) equation of Lorenz type chaos system i is:

$\left\{\begin{array}{c}\mathrm{dx}/\mathrm{dt}=a(y-x)\\ \mathrm{dy}/\mathrm{dt}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ \mathrm{dz}/\mathrm{dt}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,i,a=20,b=14,c=10.6,h=2.8$

The equation of (2) 0.9 rank Lorenz type chaos system ii is:

$\left\{\begin{array}{c}{d}^{0.9}x/{\mathrm{dt}}^{0.9}=a(y-x)\\ d^{0.9}y/{\mathrm{dt}}^{0.9}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{0.9}z/{\mathrm{dt}}^{0.9}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,\mathrm{ii},a=20,b=14,c=10.6,h=2.8$

The equation of (3) 0.1 rank Lorenz type chaos system iii is:

$\left\{\begin{array}{c}{d}^{0.1}x/{\mathrm{dt}}^{0.1}=a(y-x)\\ d^{0.1}y/{\mathrm{dt}}^{0.1}=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{0.1}z/{\mathrm{dt}}^{0.1}=\mathrm{xy}-\mathrm{hz}\end{array}\right.,\mathrm{iii},a=20,b=14,c=10.6,h=2.8$

(4) structure switching function q=f (x), wherein the expression formula iv of f (x) is:

$q=f\left(x\right)=\left\{\begin{array}{cc}0.9& x>0\\ 0.1& x\≤0\end{array}\right.,\mathrm{iv}$

(5) constructing the different Lorenz type chaos switched system v of a kind of fractional-order by ii, iii and iv is:

$\left\{\begin{array}{c}{d}^{q}x/{\mathrm{dt}}^q=a(y-x)\\ d^{q}y/{\mathrm{dt}}^q=\mathrm{bx}+\mathrm{cy}-\mathrm{xz}\\ d^{q}z/{\mathrm{dt}}^q=\mathrm{xy}-\mathrm{hz}\end{array}\right.,a=20,b=14,c=10.6,h=2.8,q=f\left(x\right)=\left\{\begin{array}{cc}0.9& x>0\\ 0.1& x\≤0\end{array}\right.,v$

(6) the Lorenz type chaos switched system v constructing analog Circuits System different according to fractional-order, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity form the fractional order inverting integrator of anti-phase adder and different orders, utilize multiplier U3 and multiplier U4 to realize multiplying, utilize analog switch U5 to realize the selection output of analog signal, described operational amplifier U1 and operational amplifier U2 adopt LF347D, described multiplier U3 and multiplier U4 adopt AD633JN, described analog switch U5 adopts ADG888, described operational amplifier U1 connects multiplier U3, multiplier U4 and analog switch U5, described operational amplifier U2 connects multiplier U3 and analog switch U5, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described analog switch U5 concatenation operation amplifier U1 and operational amplifier U2,

The 1st pin of described operational amplifier U1 joins by resistance R 3 and the 2nd pin of operational amplifier U1, join by resistance R 8 and the 6th pin of operational amplifier U1, the 3rd of operational amplifier U1, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin of operational amplifier U1 is in parallel by resistance R y11 and capacitor C y11's, connecting resistance Ry12 is in parallel with capacitor C y12's, again after connecting resistance Ry13 and capacitor C y13 in parallel, connect again the 7th pin of analog switch U5, in parallel by resistance R y21 and capacitor C y21, connecting resistance Ry22 is in parallel with capacitor C y22's, again after connecting resistance Ry23 and capacitor C y23 in parallel, connect again the 5th pin of analog switch U5, the 7th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 2, connect the 6th pin of operational amplifier U1 by resistance R 4, connect the 3rd pin of multiplier U4, the 8th pin of operational amplifier U1 connects the 2nd pin of operational amplifier U1 by resistance R 5, connect the 9th pin of operational amplifier U1 by resistance R 6, connect the 2nd pin of operational amplifier U2, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, the 9th pin of operational amplifier U1 is in parallel by resistance R x11 and capacitor C x11's, connecting resistance Rx12 is in parallel with capacitor C x12's, again after connecting resistance Rx13 and capacitor C x13 in parallel, connect again the 2nd pin of analog switch U5, in parallel by resistance R x21 and capacitor C x21, connecting resistance Rx22 is in parallel with capacitor C x22's, again after connecting resistance Rx23 and capacitor C x23 in parallel, connect again the 4th pin of analog switch U5, the 14th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 1, connect the 9th pin of operational amplifier U1 by resistance R 7,

The 6th of described operational amplifier U2, 7 pins are unsettled, the 3rd of described operational amplifier U2, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 1st pin of operational amplifier U2 is by the series connection ground connection of resistance R 14 and R15, meet the 8th of analog switch U5 by R14, 9 pins, the 8th pin of operational amplifier U2 connects the 9th pin of operational amplifier U2 by resistance R 12, connect the 3rd pin of multiplier U3, the 9th pin of operational amplifier U2 is in parallel by resistance R z11 and capacitor C z11's, connecting resistance Rz12 is in parallel with capacitor C z12's, again after connecting resistance Rz13 and capacitor C z13 in parallel, connect again the 10th pin of analog switch U5, in parallel by resistance R z21 and capacitor C z21, connecting resistance Rz22 is in parallel with capacitor C z22's, again after connecting resistance Rz23 and capacitor C z23 in parallel, connect again the 12nd pin of analog switch U5, the 14th pin of operational amplifier U2 connects the 13rd pin of operational amplifier U2 by resistance R 11, connect the 9th pin of operational amplifier U2 by resistance R 13,

The 1st pin of described multiplier U3 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 8th pin of operational amplifier U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 6th pin of operational amplifier U1 by resistance R 9, the 8th pin meets VCC;

The 1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 7th pin of operational amplifier U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance R 10, the 8th pin meets VCC;

The 1st pin of described analog switch U5 meets VCC, the 16th pin ground connection, and the 13rd, 14,15 pins are unsettled, and the 3rd pin connects the 8th pin of operational amplifier U1, and the 6th pin connects the 7th pin of operational amplifier U1, and the 11st pin connects the 8th pin of operational amplifier U2.

2. the Lorenz type chaos switched system circuit that fractional-order is different, it is characterized in that being, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity form the fractional order inverting integrator of anti-phase adder and different orders, utilize multiplier U3 and multiplier U4 to realize multiplying, utilize analog switch U5 to realize the selection output of analog signal, described operational amplifier U1 and operational amplifier U2 adopt LF347D, described multiplier U3 and multiplier U4 adopt AD633JN, described analog switch U5 adopts ADG888, described operational amplifier U1 connects multiplier U3, multiplier U4 and analog switch U5, described operational amplifier U2 connects multiplier U3 and analog switch U5, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described analog switch U5 concatenation operation amplifier U1 and operational amplifier U2,

The 1st pin of described operational amplifier U1 joins by resistance R 3 and the 2nd pin of operational amplifier U1, join by resistance R 8 and the 6th pin of operational amplifier U1, the 3rd of operational amplifier U1, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin of operational amplifier U1 is in parallel by resistance R y11 and capacitor C y11's, connecting resistance Ry12 is in parallel with capacitor C y12's, again after connecting resistance Ry13 and capacitor C y13 in parallel, connect again the 7th pin of analog switch U5, in parallel by resistance R y21 and capacitor C y21, connecting resistance Ry22 is in parallel with capacitor C y22's, again after connecting resistance Ry23 and capacitor C y23 in parallel, connect again the 5th pin of analog switch U5, the 7th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 2, connect the 6th pin of operational amplifier U1 by resistance R 4, connect the 3rd pin of multiplier U4, the 8th pin of operational amplifier U1 connects the 2nd pin of operational amplifier U1 by resistance R 5, connect the 9th pin of operational amplifier U1 by resistance R 6, connect the 2nd pin of operational amplifier U2, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, the 9th pin of operational amplifier U1 is in parallel by resistance R x11 and capacitor C x11's, connecting resistance Rx12 is in parallel with capacitor C x12's, again after connecting resistance Rx13 and capacitor C x13 in parallel, connect again the 2nd pin of analog switch U5, in parallel by resistance R x21 and capacitor C x21, connecting resistance Rx22 is in parallel with capacitor C x22's, again after connecting resistance Rx23 and capacitor C x23 in parallel, connect again the 4th pin of analog switch U5, the 14th pin of operational amplifier U1 connects the 13rd pin of operational amplifier U1 by resistance R 1, connect the 9th pin of operational amplifier U1 by resistance R 7,

The 6th of described operational amplifier U2, 7 pins are unsettled, the 3rd of described operational amplifier U2, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 1st pin of operational amplifier U2 is by the series connection ground connection of resistance R 14 and R15, meet the 8th of analog switch U5 by R14, 9 pins, the 8th pin of operational amplifier U2 connects the 9th pin of operational amplifier U2 by resistance R 12, connect the 3rd pin of multiplier U3, the 9th pin of operational amplifier U2 is in parallel by resistance R z11 and capacitor C z11's, connecting resistance Rz12 is in parallel with capacitor C z12's, again after connecting resistance Rz13 and capacitor C z13 in parallel, connect again the 10th pin of analog switch U5, in parallel by resistance R z21 and capacitor C z21, connecting resistance Rz22 is in parallel with capacitor C z22's, again after connecting resistance Rz23 and capacitor C z23 in parallel, connect again the 12nd pin of analog switch U5, the 14th pin of operational amplifier U2 connects the 13rd pin of operational amplifier U2 by resistance R 11, connect the 9th pin of operational amplifier U2 by resistance R 13,

The 1st pin of described multiplier U3 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 8th pin of operational amplifier U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 6th pin of operational amplifier U1 by resistance R 9, the 8th pin meets VCC;

The 1st pin of described multiplier U4 connects the 8th pin of operational amplifier U1, the 3rd pin connects the 7th pin of operational amplifier U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, the 7th pin connects the 13rd pin of operational amplifier U2 by resistance R 10, the 8th pin meets VCC;

The 1st pin of described analog switch U5 meets VCC, the 16th pin ground connection, and the 13rd, 14,15 pins are unsettled, and the 3rd pin connects the 8th pin of operational amplifier U1, and the 6th pin connects the 7th pin of operational amplifier U1, and the 11st pin connects the 8th pin of operational amplifier U2.

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