CN104486062A - Implementation of 0.4-order Liu chaotic system circuit based on T-shaped fractional order integration circuit module - Google Patents

Abstract

The invention provides implementation of a 0.4-order Liu chaotic system circuit based on a T-shaped fractional order integration circuit module. The T-shaped fractional order integration circuit module comprises six parts, wherein a first part is formed by connecting four resistors in series with a potentiometer and then connecting the four resistors in parallel with four capacitors; the subsequent five parts are formed by connecting the four resistors in series with the potentiometer and then connecting the four resistors in parallel with the four capacitors. According to the implementation of the 0.4-order Liu chaotic system circuit based on the T-shaped fractional order integration circuit module, the T-shaped structure is used; a PCB (Printed Circuit Board) circuit is designed and manufactured; the 0.4-order fractional order integration circuit is formed by six parts; the 0.4-order Liu chaotic system circuit implemented by the method is high in reliability and has low possibility of making error.

Description

Based on 0.4 rank Liu chaos system circuit realiration of T-shaped fractional order integration circuit module

Technical field

The present invention relates to a kind of general score rank integrating circuit module and 0.4 rank chaos system circuit realiration thereof, particularly 0.4 rank Liu chaos system of a general score rank integrating circuit module based on T-type structure and analog circuit realize.

Background technology

Because the resistance and the electric capacity that realize the circuit of chaotic systems with fractional order are all non-conventional resistive and electric capacity, the method of general employing resistant series and Capacitance parallel connection realizes, at present, the main method realized is the method utilizing existing resistance and electric capacity to combine on bread board, this method reliability and stability are lower, and exist and easily make mistakes, the not problem such as easy-to-search after makeing mistakes, the present invention is for overcoming this problem, adopt T-type structure, design and produce PCB circuit, whole circuit is made up of six parts, after Part I is connected by four resistance and a potentiometer, form with four Capacitance parallel connections, five parts next are by after four resistance and a potentiometer series connection, be in series with four Capacitance parallel connection parts and form, 0.4 rank fractional order integration circuit is made up of six parts, adopt in this way realize 0.4 rank fractional order chaotic system circuit, reliability is high, not easily make mistakes.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of 0.4 rank Liu chaos system and analog circuit realization of the fractional order integration circuit module based on T-type structure, and the present invention adopts following technological means to realize goal of the invention:

1, a T-shaped general score rank integrating circuit module, is characterized in that being: resistance Rx is in parallel with electric capacity Cx, forms Part I, resistance Ry connects with electric capacity Cy, and form Part II, resistance Rz connects with electric capacity Cz, form Part III, resistance Rw connects with electric capacity Cw, and form Part IV, resistance Ru connects with electric capacity Cu, form Part V, resistance Rv connects with electric capacity Cv, forms Part VI, and Part I and below five parts are for being connected in parallel.

2, a kind of T-shaped general score rank integrating circuit module according to claim 1, it is characterized in that: described resistance Rx is composed in series by potentiometer Rx1 and resistance Rx2, Rx3, Rx4, Rx5, described electric capacity Cx is composed in parallel by electric capacity Cx1, Cx2, Cx3, Cx4; Described resistance Ry is composed in series by potentiometer Ry1 and resistance Ry2, Ry3, Ry4, Ry5, and described electric capacity Cy, by electric capacity Cy1, Cy2, Cy3, Cy4, composes in parallel; Described resistance Rz is composed in series by potentiometer Rz1 and resistance Rz2, Rz3, Rz4, Rz5, and described electric capacity Cz is composed in parallel by electric capacity Cz1, Cz2, Cz3, Cz4; Described resistance Rw is composed in series by potentiometer Rw1 and resistance Rw2, Rw3, Rw4, Rw5, and described electric capacity Cw is composed in parallel by electric capacity Cw1, Cw2, Cw3, Cw4; Described resistance Ru is composed in series by potentiometer Ru1 and resistance Ru2, Ru3, Ru4, Ru5, and described electric capacity Cu is composed in parallel by electric capacity Cu1, Cu2, Cu3, Cu4; Described resistance Rv is composed in series by potentiometer Rv1 and resistance Rv2, Rv3, Rv4, Rv5, and described electric capacity Cv is composed in parallel by electric capacity Cv1, Cv2, Cv3, Cv4.

3, a kind of T-shaped general score rank integrating circuit module according to claim 1, described 0.4 rank integrating circuit module, it is characterized in that: described resistance Rx=6.310M, described potentiometer Rx1=0K, described resistance Rx2=6.2M, Rx3=100K, Rx4=10K, Rx5=0K, described electric capacity Cx=0.02818uF, described electric capacity Cx1=22nF, Cx2=6.8nF, Cx3 are unsettled, Cx4=is unsettled; Described resistance Ry=7.026M, described potentiometer Ry1=4K, described resistance Ry2=6.8M, Ry3=200K, Ry4=20K, Ry5=2K, described electric capacity Cy=3.715uF, described electric capacity Cy1=3.3uF, Cy2=330nF, Cy3=68nF, Cy4=22nF; Described resistance Rz=2.990M, described potentiometer Rz1=0K and described resistance Rz2=2.2M, Rz3=500K, Rz4=270K, Rz5=20K, described electric capacity Cz=1.281uF, described electric capacity Cz1=1uF, Cz2=220nF, Cz3=68nF, Cz4 are unsettled; Described resistance Rw=1.375M, described potentiometer Rw1=0K and described resistance Rw2=1M, Rw3=270K, Rw4=100K, Rw5=5K, described electric capacity Cw=0.4091uF, described electric capacity Cw1=330nF, Cw2=68nF, Cw32.2nF, Cw4 are unsettled; Described resistance Ru=0.6461M, described potentiometer Ru1=0K and described resistance Ru2=620K, Ru3=20K, Ru4=5.1K, Ru5=1K, described electric capacity Cu=0.1277uF, described electric capacity Cu1=100nF, Cu2=22nF, Cu3=4.7nF, Cu4=1nF; Described resistance Rv=0.3351M, described potentiometer Rv1=K and described resistance Rv2=330K, Rv3=5.1K, Rv4=0K, Rv5=0K, described electric capacity Cv=0.03616uF, described electric capacity Cv1=33nF, Cv2=3.3nF, Cv3 are unsettled, Cv4 is unsettled.

4, based on 0.4 rank Liu chaos system circuit of T-shaped fractional order integration circuit module, it is characterized in that:

(1) Liu chaos system i is:

$\left\{\begin{array}{ccc}\frac{\mathrm{dx}}{\mathrm{dt}}=a(y-x)& & \\ \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{bx}-\mathrm{cxz}& i& a=10,b=20,c=1,d=2.5,h=4\\ \frac{\mathrm{dz}}{\mathrm{dt}}={\mathrm{hx}}^2-\mathrm{dz}& & \end{array}\right.$

(2) 0.4 rank Liu chaos system ii are:

$\left\{\begin{array}{ccc}\frac{d^{\mathrm{\α}}x}{{\mathrm{dt}}^{\mathrm{\α}}}=a(y-x)& & \\ \frac{d^{\mathrm{\α}}y}{{\mathrm{dt}}^{\mathrm{\α}}}=\mathrm{bx}-\mathrm{cxz}& \mathrm{ii}& a=10,b=20,c=1,d=2.5,h=4,\mathrm{\α}=0.4\\ \frac{d^{\mathrm{\α}}z}{{\mathrm{dt}}^{\mathrm{\α}}}={\mathrm{hx}}^2-\mathrm{dz}& & \end{array}\right.$

(3) according to 0.4 rank Liu chaos system ii constructing analog circuit, operational amplifier U1, operational amplifier U2 and resistance and 0.4 rank integrating circuit module U5,0.4 rank integrating circuit module U6,0.4 rank integrating circuit module U7 is utilized to form anti-phase adder and anti-phase 0.4 rank integrator, multiplier U3 and multiplier U4 is utilized to realize multiplying, described operational amplifier U1 and operational amplifier U2 adopts LF347N, described multiplier U3 and multiplier U4 to adopt AD633JN;

Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, multiplier U4 and 0.4 rank integrating circuit module U5,0.4 rank integrating circuit module U6, described operational amplifier U2 connects multiplier U3, multiplier U4 and 0.4 rank integrating circuit module U7, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2;

1st pin of described operational amplifier U1 is connected by the 6th pin of resistance R8 and U1, 2nd pin is connected with the 1st pin by resistance R6, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, the P pin of the 6th pin chain link formula fractional order integration circuit U 7, 7th pin connects and exports y, connected with the 13rd pin by resistance R1, the P2 pin of chain link formula fractional order integration circuit U 8, 8th pin connects and exports x, connected with the 9th pin by resistance R4, connected with the 2nd pin by resistance R5, connect the 1st pin of multiplier U3, connect the 1st and the 3rd pin of multiplier U4, the P2 pin of chain link formula fractional order integration circuit U 6, the P pin of the 9th pin chain link formula fractional order integration circuit U 5, 13rd pin is connected with the 14th pin by resistance R2, 14th pin is connected with the 9th pin by resistance R3,

Described operational amplifier U2 the 1st, 2,6,7 pins are unsettled, 3rd, 5,10,12 pin ground connection, 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin exports z, connected with the 9th pin by resistance R12, connect the 3rd pin of multiplier U3, the P2 pin of chain link formula fractional order integration circuit U 10, the P pin of the 9th pin chain link formula fractional order integration circuit U 9,13rd pin connects the 14th pin by resistance R10, and the 14th pin connects the 9th pin by resistance R11;

1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R7, and the 8th pin meets VCC;

1st and the 3rd pin of described multiplier U4 connects the 8th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R9, and the 8th pin meets VCC.

The A pin of described 0.4 rank integrating circuit module U5 connects the 9th pin of operational amplifier U1, and B pin connects the 8th pin of operational amplifier U1;

The A pin of described 0.4 rank integrating circuit module U6 connects the 6th pin of operational amplifier U1, and B pin connects the 7th pin of operational amplifier U1;

The A pin of described 0.4 rank integrating circuit module U7 connects the 9th pin of operational amplifier U2, and B pin connects the 8th pin of operational amplifier U2.

The invention has the beneficial effects as follows: adopt T-type structure, design and produce PCB circuit, circuit is made up of six parts, and Part I forms with four Capacitance parallel connections after being connected by four resistance and a potentiometer, five parts next are by after four resistance and a potentiometer series connection, be in series with four Capacitance parallel connection parts and form, T-shaped 0.4 rank General integral circuit is made up of six parts, adopt in this way realize 0.4 rank fractional order chaotic system circuit, reliability is high, not easily makes mistakes.

Accompanying drawing explanation

Fig. 1 is T-shaped fractional order integration circuit module internal structure schematic diagram (a) of the present invention, inner actual connection layout (b) and 0.4 rank integrating circuit module map (c).

Fig. 2 is the circuit connection structure schematic diagram of the preferred embodiment of the present invention.

Fig. 3 and Fig. 4 is 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, see Fig. 1-Fig. 4.

1, a T-shaped general score rank integrating circuit module, is characterized in that being: resistance Rx is in parallel with electric capacity Cx, forms Part I, resistance Ry connects with electric capacity Cy, and form Part II, resistance Rz connects with electric capacity Cz, form Part III, resistance Rw connects with electric capacity Cw, and form Part IV, resistance Ru connects with electric capacity Cu, form Part V, resistance Rv connects with electric capacity Cv, forms Part VI, and Part I and below five parts are for being connected in parallel.

2, a kind of T-shaped general score rank integrating circuit module according to claim 1, it is characterized in that: described resistance Rx is composed in series by potentiometer Rx1 and resistance Rx2, Rx3, Rx4, Rx5, described electric capacity Cx is composed in parallel by electric capacity Cx1, Cx2, Cx3, Cx4; Described resistance Ry is composed in series by potentiometer Ry1 and resistance Ry2, Ry3, Ry4, Ry5, and described electric capacity Cy, by electric capacity Cy1, Cy2, Cy3, Cy4, composes in parallel; Described resistance Rz is composed in series by potentiometer Rz1 and resistance Rz2, Rz3, Rz4, Rz5, and described electric capacity Cz is composed in parallel by electric capacity Cz1, Cz2, Cz3, Cz4; Described resistance Rw is composed in series by potentiometer Rw1 and resistance Rw2, Rw3, Rw4, Rw5, and described electric capacity Cw is composed in parallel by electric capacity Cw1, Cw2, Cw3, Cw4; Described resistance Ru is composed in series by potentiometer Ru1 and resistance Ru2, Ru3, Ru4, Ru5, and described electric capacity Cu is composed in parallel by electric capacity Cu1, Cu2, Cu3, Cu4; Described resistance Rv is composed in series by potentiometer Rv1 and resistance Rv2, Rv3, Rv4, Rv5, and described electric capacity Cv is composed in parallel by electric capacity Cv1, Cv2, Cv3, Cv4.

3, a kind of T-shaped general score rank integrating circuit module according to claim 1, described 0.4 rank integrating circuit module, it is characterized in that: described resistance Rx=6.310M, described potentiometer Rx1=0K, described resistance Rx2=6.2M, Rx3=100K, Rx4=10K, Rx5=0K, described electric capacity Cx=0.02818uF, described electric capacity Cx1=22nF, Cx2=6.8nF, Cx3 are unsettled, Cx4=is unsettled; Described resistance Ry=7.026M, described potentiometer Ry1=4K, described resistance Ry2=6.8M, Ry3=200K, Ry4=20K, Ry5=2K, described electric capacity Cy=3.715uF, described electric capacity Cy1=3.3uF, Cy2=330nF, Cy3=68nF, Cy4=22nF; Described resistance Rz=2.990M, described potentiometer Rz1=0K and described resistance Rz2=2.2M, Rz3=500K, Rz4=270K, Rz5=20K, described electric capacity Cz=1.281uF, described electric capacity Cz1=1uF, Cz2=220nF, Cz3=68nF, Cz4 are unsettled; Described resistance Rw=1.375M, described potentiometer Rw1=0K and described resistance Rw2=1M, Rw3=270K, Rw4=100K, Rw5=5K, described electric capacity Cw=0.4091uF, described electric capacity Cw1=330nF, Cw2=68nF, Cw32.2nF, Cw4 are unsettled; Described resistance Ru=0.6461M, described potentiometer Ru1=0K and described resistance Ru2=620K, Ru3=20K, Ru4=5.1K, Ru5=1K, described electric capacity Cu=0.1277uF, described electric capacity Cu1=100nF, Cu2=22nF, Cu3=4.7nF, Cu4=1nF; Described resistance Rv=0.3351M, described potentiometer Rv1=K and described resistance Rv2=330K, Rv3=5.1K, Rv4=0K, Rv5=0K, described electric capacity Cv=0.03616uF, described electric capacity Cv1=33nF, Cv2=3.3nF, Cv3 are unsettled, Cv4 is unsettled.

4, based on 0.4 rank Liu chaos system circuit of T-shaped fractional order integration circuit module, it is characterized in that:

(1) Liu chaos system i is:

$\left\{\begin{array}{ccc}\frac{\mathrm{dx}}{\mathrm{dt}}=a(y-x)& & \\ \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{bx}-\mathrm{cxz}& i& a=10,b=20,c=1,d=2.5,h=4\\ \frac{\mathrm{dz}}{\mathrm{dt}}={\mathrm{hx}}^2-\mathrm{dz}& & \end{array}\right.$

(2) 0.4 rank Liu chaos system ii are:

$\left\{\begin{array}{ccc}\frac{d^{\mathrm{\α}}x}{{\mathrm{dt}}^{\mathrm{\α}}}=a(y-x)& & \\ \frac{d^{\mathrm{\α}}y}{{\mathrm{dt}}^{\mathrm{\α}}}=\mathrm{bx}-\mathrm{cxz}& \mathrm{ii}& a=10,b=20,c=1,d=2.5,h=4,\mathrm{\α}=0.4\\ \frac{d^{\mathrm{\α}}z}{{\mathrm{dt}}^{\mathrm{\α}}}={\mathrm{hx}}^2-\mathrm{dz}& & \end{array}\right.$

(3) according to 0.4 rank Liu chaos system ii constructing analog circuit, operational amplifier U1, operational amplifier U2 and resistance and 0.4 rank integrating circuit module U5,0.4 rank integrating circuit module U6,0.4 rank integrating circuit module U7 is utilized to form anti-phase adder and anti-phase 0.4 rank integrator, multiplier U3 and multiplier U4 is utilized to realize multiplying, described operational amplifier U1 and operational amplifier U2 adopts LF347N, described multiplier U3 and multiplier U4 to adopt AD633JN;

Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, multiplier U4 and 0.4 rank integrating circuit module U5,0.4 rank integrating circuit module U6, described operational amplifier U2 connects multiplier U3, multiplier U4 and 0.4 rank integrating circuit module U7, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2;

1st pin of described operational amplifier U1 is connected by the 6th pin of resistance R8 and U1, 2nd pin is connected with the 1st pin by resistance R6, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, the P pin of the 6th pin chain link formula fractional order integration circuit U 7, 7th pin connects and exports y, connected with the 13rd pin by resistance R1, the P2 pin of chain link formula fractional order integration circuit U 8, 8th pin connects and exports x, connected with the 9th pin by resistance R4, connected with the 2nd pin by resistance R5, connect the 1st pin of multiplier U3, connect the 1st and the 3rd pin of multiplier U4, the P2 pin of chain link formula fractional order integration circuit U 6, the P pin of the 9th pin chain link formula fractional order integration circuit U 5, 13rd pin is connected with the 14th pin by resistance R2, 14th pin is connected with the 9th pin by resistance R3,

Described operational amplifier U2 the 1st, 2,6,7 pins are unsettled, 3rd, 5,10,12 pin ground connection, 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin exports z, connected with the 9th pin by resistance R12, connect the 3rd pin of multiplier U3, the P2 pin of chain link formula fractional order integration circuit U 10, the P pin of the 9th pin chain link formula fractional order integration circuit U 9,13rd pin connects the 14th pin by resistance R10, and the 14th pin connects the 9th pin by resistance R11;

1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R7, and the 8th pin meets VCC;

1st and the 3rd pin of described multiplier U4 connects the 8th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R9, and the 8th pin meets VCC.

The A pin of described 0.4 rank integrating circuit module U5 connects the 9th pin of operational amplifier U1, and B pin connects the 8th pin of operational amplifier U1;

The A pin of described 0.4 rank integrating circuit module U6 connects the 6th pin of operational amplifier U1, and B pin connects the 7th pin of operational amplifier U1;

The A pin of described 0.4 rank integrating circuit module U7 connects the 9th pin of operational amplifier U2, and B pin connects the 8th pin of operational amplifier U2.

Resistance R1=R2=R3=R4=R6=R8=R10=R11=10k, Ω R5=5k Ω in circuit, R7=1k Ω, R9=0.25k Ω, R12=40k Ω.

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 (4)

1. a T-shaped general score rank integrating circuit module, is characterized in that being: resistance Rx is in parallel with electric capacity Cx, forms Part I, resistance Ry connects with electric capacity Cy, and form Part II, resistance Rz connects with electric capacity Cz, form Part III, resistance Rw connects with electric capacity Cw, and form Part IV, resistance Ru connects with electric capacity Cu, form Part V, resistance Rv connects with electric capacity Cv, forms Part VI, and Part I and below five parts are for being connected in parallel.

2. a kind of T-shaped general score rank integrating circuit module according to claim 1, it is characterized in that: described resistance Rx is composed in series by potentiometer Rx1 and resistance Rx2, Rx3, Rx4, Rx5, described electric capacity Cx is composed in parallel by electric capacity Cx1, Cx2, Cx3, Cx4; Described resistance Ry is composed in series by potentiometer Ry1 and resistance Ry2, Ry3, Ry4, Ry5, and described electric capacity Cy, by electric capacity Cy1, Cy2, Cy3, Cy4, composes in parallel; Described resistance Rz is composed in series by potentiometer Rz1 and resistance Rz2, Rz3, Rz4, Rz5, and described electric capacity Cz is composed in parallel by electric capacity Cz1, Cz2, Cz3, Cz4; Described resistance Rw is composed in series by potentiometer Rw1 and resistance Rw2, Rw3, Rw4, Rw5, and described electric capacity Cw is composed in parallel by electric capacity Cw1, Cw2, Cw3, Cw4; Described resistance Ru is composed in series by potentiometer Ru1 and resistance Ru2, Ru3, Ru4, Ru5, and described electric capacity Cu is composed in parallel by electric capacity Cu1, Cu2, Cu3, Cu4; Described resistance Rv is composed in series by potentiometer Rv1 and resistance Rv2, Rv3, Rv4, Rv5, and described electric capacity Cv is composed in parallel by electric capacity Cv1, Cv2, Cv3, Cv4.

3. a kind of T-shaped general score rank integrating circuit module according to claim 1, described 0.4 rank integrating circuit module, it is characterized in that: described resistance Rx=6.310M, described potentiometer Rx1=0K, described resistance Rx2=6.2M, Rx3=100K, Rx4=10K, Rx5=0K, described electric capacity Cx=0.02818uF, described electric capacity Cx1=22nF, Cx2=6.8nF, Cx3 are unsettled, Cx4=is unsettled; Described resistance Ry=7.026M, described potentiometer Ry1=4K, described resistance Ry2=6.8M, Ry3=200K, Ry4=20K, Ry5=2K, described electric capacity Cy=3.715uF, described electric capacity Cy1=3.3uF, Cy2=330nF, Cy3=68nF, Cy4=22nF; Described resistance Rz=2.990M, described potentiometer Rz1=0K and described resistance Rz2=2.2M, Rz3=500K, Rz4=270K, Rz5=20K, described electric capacity Cz=1.281uF, described electric capacity Cz1=1uF, Cz2=220nF, Cz3=68nF, Cz4 are unsettled; Described resistance Rw=1.375M, described potentiometer Rw1=0K and described resistance Rw2=1M, Rw3=270K, Rw4=100K, Rw5=5K, described electric capacity Cw=0.4091uF, described electric capacity Cw1=330nF, Cw2=68nF, Cw32.2nF, Cw4 are unsettled; Described resistance Ru=0.6461M, described potentiometer Ru1=0K and described resistance Ru2=620K, Ru3=20K, Ru4=5.1K, Ru5=1K, described electric capacity Cu=0.1277uF, described electric capacity Cu1=100nF, Cu2=22nF, Cu3=4.7nF, Cu4=1nF; Described resistance Rv=0.3351M, described potentiometer Rv1=K and described resistance Rv2=330K, Rv3=5.1K, Rv4=0K, Rv5=0K, described electric capacity Cv=0.03616uF, described electric capacity Cv1=33nF, Cv2=3.3nF, Cv3 are unsettled, Cv4 is unsettled.

4., based on 0.4 rank Liu chaos system circuit of T-shaped fractional order integration circuit module, it is characterized in that:

(1) Liu chaos system i is:

$\left\{\begin{array}{ccc}\frac{\mathrm{dx}}{\mathrm{dt}}=a(y-x)& & \\ \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{bx}-\mathrm{cxz}& i& a=10,b=20,c=1,d=2.5,h=4\\ \frac{\mathrm{dz}}{\mathrm{dt}}={\mathrm{hx}}^2-\mathrm{dz}& & \end{array}\right.$

(2) 0.4 rank Liu chaos system ii are:

$\left\{\begin{array}{ccc}\frac{d^{\mathrm{\α}}x}{{\mathrm{dt}}^{\mathrm{\α}}}=a(y-x)& & \\ \frac{d^{\mathrm{\α}}y}{{\mathrm{dt}}^{\mathrm{\α}}}=\mathrm{bx}-\mathrm{cxz}& \mathrm{ii}& a=10,b=20,c=1,d=2.5,h=4,\mathrm{\α}=0.4\\ \frac{d^{\mathrm{\α}}z}{{\mathrm{dt}}^{\mathrm{\α}}}={\mathrm{hx}}^2-\mathrm{dz}& & \end{array}\right.$

(3) according to 0.4 rank Liu chaos system ii constructing analog circuit, operational amplifier U1, operational amplifier U2 and resistance and 0.4 rank integrating circuit module U5,0.4 rank integrating circuit module U6,0.4 rank integrating circuit module U7 is utilized to form anti-phase adder and anti-phase 0.4 rank integrator, multiplier U3 and multiplier U4 is utilized to realize multiplying, described operational amplifier U1 and operational amplifier U2 adopts LF347N, described multiplier U3 and multiplier U4 to adopt AD633JN;

Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, multiplier U4 and 0.4 rank integrating circuit module U5,0.4 rank integrating circuit module U6, described operational amplifier U2 connects multiplier U3, multiplier U4 and 0.4 rank integrating circuit module U7, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2;

1st pin of described operational amplifier U1 is connected by the 6th pin of resistance R8 and U1, 2nd pin is connected with the 1st pin by resistance R6, 3rd, 5, 10, 12 pin ground connection, 4th pin meets VCC, 11st pin meets VEE, the P pin of the 6th pin chain link formula fractional order integration circuit U 7, 7th pin connects and exports y, connected with the 13rd pin by resistance R1, the P2 pin of chain link formula fractional order integration circuit U 8, 8th pin connects and exports x, connected with the 9th pin by resistance R4, connected with the 2nd pin by resistance R5, connect the 1st pin of multiplier U3, connect the 1st and the 3rd pin of multiplier U4, the P2 pin of chain link formula fractional order integration circuit U 6, the P pin of the 9th pin chain link formula fractional order integration circuit U 5, 13rd pin is connected with the 14th pin by resistance R2, 14th pin is connected with the 9th pin by resistance R3,

Described operational amplifier U2 the 1st, 2,6,7 pins are unsettled, 3rd, 5,10,12 pin ground connection, 4th pin meets VCC, and the 11st pin meets VEE, and the 8th pin exports z, connected with the 9th pin by resistance R12, connect the 3rd pin of multiplier U3, the P2 pin of chain link formula fractional order integration circuit U 10, the P pin of the 9th pin chain link formula fractional order integration circuit U 9,13rd pin connects the 14th pin by resistance R10, and the 14th pin connects the 9th pin by resistance R11;

1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R7, and the 8th pin meets VCC;

1st and the 3rd pin of described multiplier U4 connects the 8th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R9, and the 8th pin meets VCC.

The A pin of described 0.4 rank integrating circuit module U5 connects the 9th pin of operational amplifier U1, and B pin connects the 8th pin of operational amplifier U1;

The A pin of described 0.4 rank integrating circuit module U6 connects the 6th pin of operational amplifier U1, and B pin connects the 7th pin of operational amplifier U1;

The A pin of described 0.4 rank integrating circuit module U7 connects the 9th pin of operational amplifier U2, and B pin connects the 8th pin of operational amplifier U2.