CN105071926B - A kind of wing chaos system circuit of singly balanced point four containing absolute value - Google Patents
A kind of wing chaos system circuit of singly balanced point four containing absolute value Download PDFInfo
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Abstract
The present invention relates to a kind of chaos system and circuit, the more particularly to a kind of wing chaos system of singly balanced point four and circuit containing absolute value.Typical chaos system such as Lorenz systems, Chen systems and Lu systems all have three equalization points, it is zero balancing point wherein to have one, another two are non-zero balancing points, attractor caused by this kind of system is double-wing chaotic attractor, four non-zero equalization points of method construct on the basis of Typical Chaotic Systems by increasing saturation function or continuous function or more equalization point, the chaos system with four wings or multiple wing attractor can be constructed, the present invention is in the case of no increase saturation function or continuous function, propose a kind of wing chaos system of singly balanced point four containing absolute value, add the type of chaos system, for chaos system a kind of new selection is provided applied to engineering practice.
Description
Technical field
The present invention relates to a kind of chaos system and circuit, more particularly to a kind of wing chaos system of singly balanced point four containing absolute value
System and circuit.
Background technology
Typical chaos system such as Lorenz systems, Chen systems and Lu systems all have three equalization points, wherein having one
Individual is zero balancing point, and another two are non-zero balancing points, and attractor caused by this kind of system is double-wing chaotic attractor, mixed in typical case
Four non-zero equalization points of method construct on the basis of ignorant system by increasing saturation function or continuous function or more balance
Point, the chaos system with four wings or multiple wing attractor can be constructed, the present invention is in no increase saturation function or continuous letter
In the case of number, it is proposed that a kind of wing chaos system of singly balanced point four containing absolute value, add the type of chaos system, be mixed
Ignorant system provides a kind of new selection applied to engineering practice.
The content of the invention
The technical problem to be solved in the present invention is to provide a kind of wing chaos system of singly balanced point four and circuit containing absolute value,
The present invention realizes goal of the invention using following technological means：
1st, a kind of wing chaos system circuit of singly balanced point four containing absolute value, it is characterised in that：
In system i, a, b, c, d, e is parameter, and f (z), f (y) are nonlinear function；
Work as a=0, b=2, c=1, d=4, e=0.5, f (z)=z2, f (y)=| y | when system i be：
System ii is a kind of wing chaos system of singly balanced point four containing absolute value；
According to system ii constructing analog circuits, operational amplifier U1, operational amplifier U2, operational amplifier U3 and electricity are utilized
Resistance and electric capacity form anti-phase adder and anti-phase fractional order integrator, are formed using operational amplifier U6 and resistance and diode exhausted
To being worth circuit, multiplying is realized using multiplier U4, multiplier U5 and multiplier U7, the operational amplifier U1, computing are put
Big device U2, operational amplifier U3 and operational amplifier U6 use LF347N, and multiplier U4, multiplier U5 and multiplier U7 are used
AD633JN；
Operational amplifier U1 concatenation operation amplifier U2 and the operational amplifier U3, the operational amplifier U2 connections fortune
Calculate amplifier U1, operational amplifier U6 and multiplier U4, the operational amplifier U3 concatenation operation amplifiers U6, multiplier U5 and
Multiplier U7, operational amplifier U6 connection multiplier U4 and multiplier U5, the multiplier U4 concatenation operations amplifier U2,
The multiplier U5 concatenation operation amplifiers U3；
The operational amplifier U1 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin meets VCC, the 11st
Pin meets VEE, and the 6th pin is connected by resistance R12 with the 7th pin, and the 7th pin meets-x, passes through resistance R4 and operational amplifier
U2 the 13rd pin connects, and is connected by resistance R18 with operational amplifier U3 the 13rd pin, the 8th pin meets x, passes through resistance
R11 connects with operational amplifier U1 the 6th pin, and the 9th pin is connected by electric capacity C1 with the 8th pin, and the 13rd pin passes through electricity
Resistance R9 connects with the 14th pin, and the 14th pin is connected by resistance R10 with the 9th pin；
The operational amplifier U2 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin meets VCC, the 11st
Pin meets VEE, and the 6th pin is connected by resistance R31 with the 7th pin, and the 7th pin meets-y, connects multiplier U4 the 3rd pin, and the 8th
Pin meets y, is connected by resistance R20 with operational amplifier U6 the 2nd pin, passes through the 6th of resistance R22 and operational amplifier U6 the
Pin connects, and is connected by resistance R2 with operational amplifier U1 the 13rd pin, passes through the of resistance R1 and operational amplifier U2
13 pins connect, and are connected by resistance R30 with operational amplifier U2 the 6th pin, the 9th pin passes through electric capacity C2 and the 8th pin
Connect, the 13rd pin is connected by resistance R5 with the 14th pin, and the 14th pin is connected by resistance R3 with the 9th pin；
The operational amplifier U3 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin meets VCC, the 11st
Pin meets VEE, and the 6th pin is connected by resistance R14 with the 7th pin, and the 7th pin meets-z, passes through resistance R8 and operational amplifier
U3 the 13rd pin connects, and the 8th pin meets z, connect multiplier U7 the 1st, 3 pins, connect multiplier U5 the 3rd pin, pass through electricity
Resistance R13 connects with operational amplifier U3 the 6th pin, is connected by resistance R6 with operational amplifier U1 the 13rd pin, the 9th draws
Pin is connected by electric capacity C3 with the 8th pin, and the 13rd pin was connected resistance R15 and connected with the 14th pin, and the 14th pin passes through electricity
Resistance R16 connects with the 9th pin；
The 1st pin of the operational amplifier U6 is connected by diode D1 with the 2nd pin, and the 2nd pin passes through resistance R21
Connecting with diode D2 with the 1st pin, the 2nd pin is connected by resistance R21 and resistance R23 with the 6th pin, and the 3rd, 5,10,12
Pin is grounded, and the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin is connected by resistance R24 with the 7th pin, and the 7th pin connects
Connect multiplier U5 the 1st pin, the 8th, 9,13,14 pins it is hanging；
The multiplier U4 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, and the 7th pin passes through resistance R17 and computing
Amplifier U2 the 13rd pin connects, and the 8th pin meets VCC；
The multiplier U5 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, and the 7th pin passes through resistance R7 and computing
Amplifier U3 the 13rd pin connects, and the 8th pin meets VCC；
The multiplier U7 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, the 1st of the 7th pin connection multiplier U4 the
Pin, the 8th pin meet VCC.
The present invention beneficial fruit be：A kind of wing chaos system of singly balanced point four containing absolute value is proposed, adds chaos
The type of system, a kind of new selection is provided applied to engineering practice for chaos system.
Brief description of the drawings
Fig. 1 is the circuit structure block diagram of the present invention.
Fig. 2 is the U1 of the present invention actual connection figure of circuit.
Fig. 3 is U2, U4 and U7 of the present invention actual connection figure of circuit.
Fig. 4 is the U3 of the present invention and U5 actual connection figure of circuit.
Fig. 5 is the U6 of the present invention actual connection figure of circuit.
Fig. 6 is the phasor in y-z directions of the present invention.
Embodiment
The present invention is further described in detail with preferred embodiment below in conjunction with the accompanying drawings, referring to Fig. 1-Fig. 6.
1st, a kind of wing chaos system circuit of singly balanced point four containing absolute value, it is characterised in that：
In system i, a, b, c, d, e is parameter, and f (z), f (y) are nonlinear function；
Work as a=0, b=2, c=1, d=4, e=0.5, f (z)=z2, f (y)=| y | when system i be：
System ii is a kind of wing chaos system of singly balanced point four containing absolute value；
According to system ii constructing analog circuits, operational amplifier U1, operational amplifier U2, operational amplifier U3 and electricity are utilized
Resistance and electric capacity form anti-phase adder and anti-phase fractional order integrator, are formed using operational amplifier U6 and resistance and diode exhausted
To being worth circuit, multiplying is realized using multiplier U4, multiplier U5 and multiplier U7, the operational amplifier U1, computing are put
Big device U2, operational amplifier U3 and operational amplifier U6 use LF347N, and multiplier U4, multiplier U5 and multiplier U7 are used
AD633JN；
Operational amplifier U1 concatenation operation amplifier U2 and the operational amplifier U3, the operational amplifier U2 connections fortune
Calculate amplifier U1, operational amplifier U6 and multiplier U4, the operational amplifier U3 concatenation operation amplifiers U6, multiplier U5 and
Multiplier U7, operational amplifier U6 connection multiplier U4 and multiplier U5, the multiplier U4 concatenation operations amplifier U2,
The multiplier U5 concatenation operation amplifiers U3；
The operational amplifier U1 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin meets VCC, the 11st
Pin meets VEE, and the 6th pin is connected by resistance R12 with the 7th pin, and the 7th pin meets-x, passes through resistance R4 and operational amplifier
U2 the 13rd pin connects, and is connected by resistance R18 with operational amplifier U3 the 13rd pin, the 8th pin meets x, passes through resistance
R11 connects with operational amplifier U1 the 6th pin, and the 9th pin is connected by electric capacity C1 with the 8th pin, and the 13rd pin passes through electricity
Resistance R9 connects with the 14th pin, and the 14th pin is connected by resistance R10 with the 9th pin；
The operational amplifier U2 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin meets VCC, the 11st
Pin meets VEE, and the 6th pin is connected by resistance R31 with the 7th pin, and the 7th pin meets-y, connects multiplier U4 the 3rd pin, and the 8th
Pin meets y, is connected by resistance R20 with operational amplifier U6 the 2nd pin, passes through the 6th of resistance R22 and operational amplifier U6 the
Pin connects, and is connected by resistance R2 with operational amplifier U1 the 13rd pin, passes through the of resistance R1 and operational amplifier U2
13 pins connect, and are connected by resistance R30 with operational amplifier U2 the 6th pin, the 9th pin passes through electric capacity C2 and the 8th pin
Connect, the 13rd pin is connected by resistance R5 with the 14th pin, and the 14th pin is connected by resistance R3 with the 9th pin；
The operational amplifier U3 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin meets VCC, the 11st
Pin meets VEE, and the 6th pin is connected by resistance R14 with the 7th pin, and the 7th pin meets-z, passes through resistance R8 and operational amplifier
U3 the 13rd pin connects, and the 8th pin meets z, connect multiplier U7 the 1st, 3 pins, connect multiplier U5 the 3rd pin, pass through electricity
Resistance R13 connects with operational amplifier U3 the 6th pin, is connected by resistance R6 with operational amplifier U1 the 13rd pin, the 9th draws
Pin is connected by electric capacity C3 with the 8th pin, and the 13rd pin was connected resistance R15 and connected with the 14th pin, and the 14th pin passes through electricity
Resistance R16 connects with the 9th pin；
The 1st pin of the operational amplifier U6 is connected by diode D1 with the 2nd pin, and the 2nd pin passes through resistance R21
Connecting with diode D2 with the 1st pin, the 2nd pin is connected by resistance R21 and resistance R23 with the 6th pin, and the 3rd, 5,10,12
Pin is grounded, and the 4th pin meets VCC, and the 11st pin meets VEE, and the 6th pin is connected by resistance R24 with the 7th pin, and the 7th pin connects
Connect multiplier U5 the 1st pin, the 8th, 9,13,14 pins it is hanging；
The multiplier U4 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, and the 7th pin passes through resistance R17 and computing
Amplifier U2 the 13rd pin connects, and the 8th pin meets VCC；
The multiplier U5 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, and the 7th pin passes through resistance R7 and computing
Amplifier U3 the 13rd pin connects, and the 8th pin meets VCC；
The multiplier U7 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, the 1st of the 7th pin connection multiplier U4 the
Pin, the 8th pin meet VCC.
Resistance R3=R5=R9=R10=R11=R12=R13=R14=R15=R16=10k Ω, R20=in circuit
R21=R22=R25=R30=R31=10k Ω, R1=R8=R23=5k Ω, R7=R17=4K Ω, R2=50K Ω, R18
=200K Ω, R4=R6=100K Ω, electric capacity C1=C2=C3=10nF in circuit.
Certainly, described above is not limitation of the present invention, and the present invention is also not limited to the example above, the art
The variations, modifications, additions or substitutions that those of ordinary skill is made in the essential scope of the present invention, fall within the guarantor of the present invention
Protect scope.
Claims (1)
- A kind of 1. wing chaos system circuit of singly balanced point four containing absolute value, it is characterised in that：<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mi>a</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> <mi>y</mi> <mo>+</mo> <mi>c</mi> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mi>x</mi> <mo>-</mo> <mrow> <mo>(</mo> <mi>f</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> <mo>-</mo> <mi>d</mi> <mo>)</mo> </mrow> <mi>y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>d</mi> <mi>z</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mi>e</mi> <mi>x</mi> <mo>+</mo> <mrow> <mo>(</mo> <mi>f</mi> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>-</mo> <mi>d</mi> <mo>)</mo> </mrow> <mi>z</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>i</mi> </mrow>In system i, a, b, c, d, e is parameter, and f (z), f (y) are nonlinear function；Work as a=0, b=2, c=1, d=4, e=0.5, f (z)=z2, f (y)=| y | when system i be：<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mi>y</mi> <mo>+</mo> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mi>x</mi> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <mo>)</mo> </mrow> <mi>y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>d</mi> <mi>z</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mn>0.5</mn> <mi>x</mi> <mo>+</mo> <mrow> <mo>(</mo> <mo>|</mo> <mi>y</mi> <mo>|</mo> <mo>-</mo> <mn>4</mn> <mo>)</mo> </mrow> <mi>z</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>i</mi> <mi>i</mi> </mrow>System ii is a kind of wing chaos system of singly balanced point four containing absolute value；According to system ii constructing analog circuits, using operational amplifier U1, operational amplifier U2, operational amplifier U3 and resistance and Electric capacity forms anti-phase adder and anti-phase fractional order integrator, and absolute value is formed using operational amplifier U6 and resistance and diode Circuit, multiplying, the operational amplifier U1, operational amplifier are realized using multiplier U4, multiplier U5 and multiplier U7 U2, operational amplifier U3 and operational amplifier U6 use LF347N, and multiplier U4, multiplier U5 and multiplier U7 are used AD633JN；Operational amplifier U1 concatenation operation amplifier U2 and the operational amplifier U3, the operational amplifier U2 concatenation operations are put Big device U1, operational amplifier U6 and multiplier U4, operational amplifier U3 concatenation operation amplifiers U6, multiplier U5 and the multiplication Device U7, operational amplifier U6 connection multiplier U4 and the multiplier U5, the multiplier U4 concatenation operation amplifiers U2, it is described Multiplier U5 concatenation operation amplifiers U3；The operational amplifier U1 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin connects VCC, the 11st pin VEE is met, the 6th pin is connected by resistance R12 with the 7th pin, and the 7th pin meets-x, passes through resistance R4's and operational amplifier U2 13rd pin connects, and is connected by resistance R18 with operational amplifier U3 the 13rd pin, and the 8th pin meets x, by resistance R11 with Operational amplifier U1 the 6th pin connects, and the 9th pin is connected by electric capacity C1 with the 8th pin, the 13rd pin by resistance R9 with 14th pin connects, and the 14th pin is connected by resistance R10 with the 9th pin；The operational amplifier U2 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin connects VCC, the 11st pin VEE is met, the 6th pin is connected by resistance R31 with the 7th pin, and the 7th pin meets-y, connects multiplier U4 the 3rd pin, the 8th pin Y is met, is connected by resistance R20 with operational amplifier U6 the 2nd pin, passes through resistance R22 and operational amplifier U6 the 6th pin Connect, connected by resistance R2 with operational amplifier U1 the 13rd pin, drawn by resistance R1 and the 13rd of operational amplifier U2 Pin connects, and is connected by resistance R30 with operational amplifier U2 the 6th pin, and the 9th pin is connected by electric capacity C2 with the 8th pin, 13rd pin is connected by resistance R5 with the 14th pin, and the 14th pin is connected by resistance R3 with the 9th pin；The operational amplifier U3 the 1st, 2 pins it is hanging, the 3rd, 5,10,12 pins ground connection, the 4th pin connects VCC, the 11st pin VEE is met, the 6th pin is connected by resistance R14 with the 7th pin, and the 7th pin meets-z, passes through resistance R8's and operational amplifier U3 13rd pin connects, and the 8th pin meets z, connect multiplier U7 the 1st, 3 pins, connect multiplier U5 the 3rd pin, pass through resistance R13 Connect with operational amplifier U3 the 6th pin, connected by resistance R6 with operational amplifier U1 the 13rd pin, the 9th pin leads to Cross electric capacity C3 with the 8th pin to connect, the 13rd pin was connected resistance R15 and with the 14th pin connected, and the 14th pin passes through resistance R16 Connect with the 9th pin；The 1st pin of the operational amplifier U6 is connected by diode D1 with the 2nd pin, and the 2nd pin passes through resistance R21 and two Pole pipe D2 connects with the 1st pin, and the 2nd pin is connected by resistance R21 and resistance R23 with the 6th pin, the 3rd, 5,10,12 pins Ground connection, the 4th pin meet VCC, and the 11st pin meets VEE, and the 6th pin is connected by resistance R24 with the 7th pin, and the connection of the 7th pin multiplies Musical instruments used in a Buddhist or Taoist mass U5 the 1st pin, the 8th, 9,13,14 pins it is hanging；The multiplier U4 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, and the 7th pin passes through resistance R17 and operation amplifier Device U2 the 13rd pin connects, and the 8th pin meets VCC；The multiplier U5 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, and the 7th pin passes through resistance R7 and operation amplifier Device U3 the 13rd pin connects, and the 8th pin meets VCC；The multiplier U7 the 2nd, 4,6 pins be grounded, the 5th pin meets VEE, and the 1st of the 7th pin connection multiplier U4 draws Pin, the 8th pin meet VCC.
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| 《一个含绝对值函数四翼混沌系统的设计与实现》;王建中;《四川兵工学报》;20131031;第34卷(第10期);第126-129页 * |
| 《三维四翼广义增广Lü系统》;乔晓华等;《物理学报》;20091231;第58卷(第12期);第8152-8159页 * |
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