CN105099660B - A kind of three equilibrium point four-winged chaotic attractor chaos circuits containing absolute value - Google Patents
A kind of three equilibrium point four-winged chaotic attractor chaos circuits containing absolute value Download PDFInfo
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Abstract
The present invention relates to a kind of chaos system and circuit, particularly to a kind of three equilibrium point four-winged chaotic attractor chaos systems containing absolute value and circuit.Typical chaos system such as Lorenz system, Chen system and Lu system all have three equilibrium points, one is wherein had to be zero balancing point, another two is non-zero balancing point, attractor produced by this kind of system is double-wing chaotic attractor, by increasing by four non-zero equilibrium points of method construct or more equilibrium points of saturation function or continuous function on the basis of Typical Chaotic Systems, the chaos system with four wings or multiple wing attractor can be constructed, the present invention is not in the case of increasing saturation function or continuous function, propose the three equilibrium point four-winged chaotic attractor chaos systems that a kind of point contains absolute value, increased the type of chaos system, it is applied to engineering practice for chaos system and provide a kind of new selection.
Description
Technical field
The present invention relates to a kind of chaos system and circuit, particularly to a kind of three equilibrium point four-winged chaotic attractor chaos containing absolute value
System and circuit.
Background technology
Typical chaos system such as Lorenz system, Chen system and Lu system all have three equilibrium points, wherein have one
It is zero balancing point, another two is non-zero balancing point, and attractor produced by this kind of system is double-wing chaotic attractor, in typical chaos
By increasing by four non-zero equilibrium points of method construct or more equilibrium points of saturation function or continuous function on the basis of system, can
To construct the chaos system with four wings or multiple wing attractor, the present invention is not increasing the situation of saturation function or continuous function
Down it is proposed that a kind of point contains three equilibrium point four-winged chaotic attractor chaos systems of absolute value, increased the type of chaos system, be mixed
Ignorant system is applied to engineering practice and provides a kind of new selection.
Content of the invention
The technical problem to be solved in the present invention is to provide a kind of three equilibrium point four-winged chaotic attractor chaos circuits containing absolute value, this
Bright realize goal of the invention using following technological means：
1st, a kind of three equilibrium point four-winged chaotic attractor chaos circuits containing absolute value it is characterised in that：
In system i, a, b, c, d, e are parameter, and f (z), f (y) are nonlinear function；
Work as a=-0.5, b=2, c=1, d=4, e=0.5, f (z)=| z |, f (y)=y2When system i be：
System ii is four wing continuous chaotic systems of three equilibrium points；According to system ii constructing analog circuit, using operational amplifier U1,
Operational amplifier U2, operational amplifier U3 and resistance and electric capacity constitute anti-phase adder and anti-phase fractional order integrator, using fortune
Calculate amplifier U6 and resistance and diode constitutes absolute value circuit, realized using multiplier U4, multiplier U5 and multiplier U7
Multiplying, described operational amplifier U1, operational amplifier U2, operational amplifier U3 and operational amplifier U6 adopt
LF347N, multiplier U4, multiplier U5 and multiplier U7 adopt AD633JN；
Described operational amplifier U1 concatenation operation amplifier U2 and operational amplifier U3, described operational amplifier U2 concatenation operation
Amplifier U1, operational amplifier U6, multiplier U4, multiplier U5 and multiplier U7, described operational amplifier U3 connects fortune
Calculate amplifier U6, multiplier U4 and multiplier U5, described operational amplifier U6 connects multiplier U4 and multiplier U5, institute
State multiplier U4 concatenation operation amplifier U2, described multiplier U5 concatenation operation amplifier U3；
1st, 2 pins of described operational amplifier U1 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R12, and the 7th pin meets output-x, passes through
Resistance R19 is connected with the 13rd pin of operational amplifier U1, by the 13rd pin phase of resistance R18 and operational amplifier U3
Connect, the 8th pin meets output x, is connected with the 6th pin of operational amplifier U1 by resistance R11, and the 9th pin passes through electricity
Hold C1 to connect with the 8th pin, the 13rd pin is connected with the 14th pin by resistance R9, the 14th pin by resistance R10 and
9 pins connect；
1st, 2 pins of described operational amplifier U2 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R31, and the 7th pin meets output-y, connects and takes advantage of
3rd pin of musical instruments used in a Buddhist or Taoist mass U4, the 8th pin meets output y, is connected with the 13rd pin of operational amplifier U1 by resistance R2,
Connected with the 13rd pin of operational amplifier U2 by resistance R1, by the 6th pin of resistance R30 and operational amplifier U2
Connect, connect the 1st pin of multiplier U7, connect the 3rd pin of multiplier U7, the 9th pin passes through electric capacity C2 and the
8 pins connect, and the 13rd pin was connected resistance R5 and connected with the 14th pin, and the 14th pin is drawn with the 9th by resistance R3
Foot connects；
1st, 2 pins of described operational amplifier U3 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R14, and the 7th pin meets output-z, passes through
Resistance R8 is connected with the 13rd pin of operational amplifier U3, and the 8th pin meets output z, connects the 3rd pin of multiplier U5,
Connected with the 6th pin of operational amplifier U3 by resistance R13, by the 13rd pin of resistance R6 and operational amplifier U1
Connect, connected with the 13rd pin of operational amplifier U6 by resistance R25, by resistance R27 and operational amplifier U6's
9th pin connects, and the 9th pin is connected with the 8th pin by electric capacity C3, and the 13rd pin connected resistance R15 and the 14th
Pin connects, and the 14th pin is connected with the 9th pin by resistance R16；
1st, 2,6,7 pins of described operational amplifier U6 are hanging, the 3rd, 5,10,12 pin ground connection, the 8th pin
Connect the 1st pin of multiplier U4, the 9th pin is connected with the 8th pin by resistance R29, the 13rd pin passes through resistance
R26 and diode D4 is connected with the 14th pin, and the 13rd pin is connected with the 9th pin by resistance R26 and resistance R28,
14th pin is connected with the 13rd pin by diode D3；
The 2nd of described multiplier U4,4,6 pins be all grounded, the 5th pin meets VEE, the 7th pin pass through resistance R17 with
Operational amplifier U2 the 13rd pin connects, and the 8th pin meets VCC；
The 2nd of described multiplier U5,4,6 pins be all grounded, the 5th pin meets VEE, the 7th pin pass through resistance R7 and fortune
The 13rd pin calculating amplifier U3 connects, and the 8th pin meets VCC；
The 2nd of described multiplier U7,4,6 pins be all grounded, the 5th pin meets VEE, and the 7th pin connects multiplier U5's
1st pin, the 8th pin meets VCC.
The beneficial fruit of the present invention is：Propose a kind of three equilibrium point four-winged chaotic attractor chaos circuits containing absolute value, increased mixed
The type of ignorant system, is that chaos system is applied to engineering practice and provides a kind of new selection.
Brief description
Fig. 1 is the circuit structure block diagram of the present invention.
Fig. 2 is the actual connection figure of circuit of U1 of the present invention.
Fig. 3 is the actual connection figure of circuit of U2 and U4 of the present invention.
Fig. 4 is the actual connection figure of circuit of U3, U5 and U7 of the present invention.
Fig. 5 is the actual connection figure of circuit of U6 of the present invention.
Fig. 6 is the phasor in y-z direction of the present invention.
Specific embodiment
With preferred embodiment, the present invention is further described in detail below in conjunction with the accompanying drawings, referring to Fig. 1-Fig. 6.
1st, a kind of three equilibrium point four-winged chaotic attractor chaos circuits containing absolute value it is characterised in that：
In system i, a, b, c, d, e are parameter, and f (z), f (y) are nonlinear function；
Work as a=-0.5, b=2, c=1, d=4, e=0.5, f (z)=| z |, f (y)=y2When system i be：
System ii is four wing continuous chaotic systems of three equilibrium points；According to system ii constructing analog circuit, using operational amplifier U1,
Operational amplifier U2, operational amplifier U3 and resistance and electric capacity constitute anti-phase adder and anti-phase fractional order integrator, using fortune
Calculate amplifier U6 and resistance and diode constitutes absolute value circuit, realized using multiplier U4, multiplier U5 and multiplier U7
Multiplying, described operational amplifier U1, operational amplifier U2, operational amplifier U3 and operational amplifier U6 adopt
LF347N, multiplier U4, multiplier U5 and multiplier U7 adopt AD633JN；
Described operational amplifier U1 concatenation operation amplifier U2 and operational amplifier U3, described operational amplifier U2 concatenation operation
Amplifier U1, operational amplifier U6, multiplier U4, multiplier U5 and multiplier U7, described operational amplifier U3 connects fortune
Calculate amplifier U6, multiplier U4 and multiplier U5, described operational amplifier U6 connects multiplier U4 and multiplier U5, institute
State multiplier U4 concatenation operation amplifier U2, described multiplier U5 concatenation operation amplifier U3；
1st, 2 pins of described operational amplifier U1 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R12, and the 7th pin meets output-x, passes through
Resistance R19 is connected with the 13rd pin of operational amplifier U1, by the 13rd pin phase of resistance R18 and operational amplifier U3
Connect, the 8th pin meets output x, is connected with the 6th pin of operational amplifier U1 by resistance R11, and the 9th pin passes through electricity
Hold C1 to connect with the 8th pin, the 13rd pin is connected with the 14th pin by resistance R9, the 14th pin by resistance R10 and
9 pins connect；
1st, 2 pins of described operational amplifier U2 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R31, and the 7th pin meets output-y, connects and takes advantage of
3rd pin of musical instruments used in a Buddhist or Taoist mass U4, the 8th pin meets output y, is connected with the 13rd pin of operational amplifier U1 by resistance R2,
Connected with the 13rd pin of operational amplifier U2 by resistance R1, by the 6th pin of resistance R30 and operational amplifier U2
Connect, connect the 1st pin of multiplier U7, connect the 3rd pin of multiplier U7, the 9th pin passes through electric capacity C2 and the
8 pins connect, and the 13rd pin was connected resistance R5 and connected with the 14th pin, and the 14th pin is drawn with the 9th by resistance R3
Foot connects；
1st, 2 pins of described operational amplifier U3 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R14, and the 7th pin meets output-z, passes through
Resistance R8 is connected with the 13rd pin of operational amplifier U3, and the 8th pin meets output z, connects the 3rd pin of multiplier U5,
Connected with the 6th pin of operational amplifier U3 by resistance R13, by the 13rd pin of resistance R6 and operational amplifier U1
Connect, connected with the 13rd pin of operational amplifier U6 by resistance R25, by resistance R27 and operational amplifier U6's
9th pin connects, and the 9th pin is connected with the 8th pin by electric capacity C3, and the 13rd pin connected resistance R15 and the 14th
Pin connects, and the 14th pin is connected with the 9th pin by resistance R16；
1st, 2,6,7 pins of described operational amplifier U6 are hanging, the 3rd, 5,10,12 pin ground connection, the 8th pin
Connect the 1st pin of multiplier U4, the 9th pin is connected with the 8th pin by resistance R29, the 13rd pin passes through resistance
R26 and diode D4 is connected with the 14th pin, and the 13rd pin is connected with the 9th pin by resistance R26 and resistance R28,
14th pin is connected with the 13rd pin by diode D3；
The 2nd of described multiplier U4,4,6 pins be all grounded, the 5th pin meets VEE, the 7th pin pass through resistance R17 with
Operational amplifier U2 the 13rd pin connects, and the 8th pin meets VCC；
The 2nd of described multiplier U5,4,6 pins be all grounded, the 5th pin meets VEE, the 7th pin pass through resistance R7 and fortune
The 13rd pin calculating amplifier U3 connects, and the 8th pin meets VCC；
The 2nd of described multiplier U7,4,6 pins be all grounded, the 5th pin meets VEE, and the 7th pin connects multiplier U5's
1st pin, the 8th pin meets VCC.
Resistance R3=R5=R9=R10=R11=R12=R13=R14=R15=R16=10k Ω in circuit,
R25=R26=R27=R29=10k Ω, R7=R17=1K Ω, R28=5k Ω, R4=R6=100k Ω,
R1=R8=25K Ω, R18=R19=200K Ω, R2=50K Ω, electric capacity C1=C2=C3=10nF in circuit.
Certainly, described above not limitation of the present invention, the present invention is also not limited to the example above, the art common
Change, remodeling, interpolation or replacement that technical staff is made in the essential scope of the present invention, fall within the protection model of the present invention
Enclose.
Claims (1)
1. a kind of three equilibrium point four-winged chaotic attractor chaos circuits containing absolute value it is characterised in that：
In system i, a, b, c, d, e are parameter, and f (z), f (y) are nonlinear function；
Work as a=-0.5, b=2, c=1, d=4, e=0.5, f (z)=| z |, f (y)=y2When system i be：
System ii is four wing continuous chaotic systems of three equilibrium points；
According to system ii constructing analog circuit, using operational amplifier U1, operational amplifier U2, operational amplifier U3 and resistance
Constitute anti-phase adder and anti-phase fractional order integrator with electric capacity, constituted definitely using operational amplifier U6 and resistance and diode
Value circuit, realizes multiplying using multiplier U4, multiplier U5 and multiplier U7, described operational amplifier U1, computing
Amplifier U2, operational amplifier U3 and operational amplifier U6 adopt LF347N, multiplier U4, multiplier U5 and multiplier
U7 adopts AD633JN；
Described operational amplifier U1 concatenation operation amplifier U2 and operational amplifier U3, described operational amplifier U2 concatenation operation
Amplifier U1, operational amplifier U6, multiplier U4, multiplier U5 and multiplier U7, described operational amplifier U3 connects fortune
Calculate amplifier U6, multiplier U4 and multiplier U5, described operational amplifier U6 connects multiplier U4 and multiplier U5, institute
State multiplier U4 concatenation operation amplifier U2, described multiplier U5 concatenation operation amplifier U3；
1st, 2 pins of described operational amplifier U1 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R12, and the 7th pin meets output-x, passes through
Resistance R19 is connected with the 13rd pin of operational amplifier U1, by the 13rd pin phase of resistance R18 and operational amplifier U3
Connect, the 8th pin meets output x, is connected with the 6th pin of operational amplifier U1 by resistance R11, and the 9th pin passes through electricity
Hold C1 to connect with the 8th pin, the 13rd pin is connected with the 14th pin by resistance R9, the 14th pin by resistance R10 and
9 pins connect；
1st, 2 pins of described operational amplifier U2 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R31, and the 7th pin meets output-y, connects and takes advantage of
3rd pin of musical instruments used in a Buddhist or Taoist mass U4, the 8th pin meets output y, is connected with the 13rd pin of operational amplifier U1 by resistance R2,
Connected with the 13rd pin of operational amplifier U2 by resistance R1, by the 6th pin of resistance R30 and operational amplifier U2
Connect, connect the 1st pin of multiplier U7, connect the 3rd pin of multiplier U7, the 9th pin passes through electric capacity C2 and the
8 pins connect, and the 13rd pin was connected resistance R5 and connected with the 14th pin, and the 14th pin is drawn with the 9th by resistance R3
Foot connects；
1st, 2 pins of described operational amplifier U3 are hanging, the 3rd, 5,10,12 pin ground connection, and the 4th pin connects
VCC, the 11st pin meets VEE, and the 6th pin is connected with the 7th pin by resistance R14, and the 7th pin meets output-z, passes through
Resistance R8 is connected with the 13rd pin of operational amplifier U3, and the 8th pin meets output z, connects the 3rd pin of multiplier U5,
Connected with the 6th pin of operational amplifier U3 by resistance R13, by the 13rd pin of resistance R6 and operational amplifier U1
Connect, connected with the 13rd pin of operational amplifier U6 by resistance R25, by resistance R27 and operational amplifier U6's
9th pin connects, and the 9th pin is connected with the 8th pin by electric capacity C3, and the 13rd pin connected resistance R15 and the 14th
Pin connects, and the 14th pin is connected with the 9th pin by resistance R16；
1st, 2,6,7 pins of described operational amplifier U6 are hanging, the 3rd, 5,10,12 pin ground connection, the 8th pin
Connect the 1st pin of multiplier U4, the 9th pin is connected with the 8th pin by resistance R29, the 13rd pin passes through resistance
R26 and diode D4 is connected with the 14th pin, and the 13rd pin is connected with the 9th pin by resistance R26 and resistance R28,
14th pin is connected with the 13rd pin by diode D3；
The 2nd of described multiplier U4,4,6 pins be all grounded, the 5th pin meets VEE, the 7th pin pass through resistance R17 with
Operational amplifier U2 the 13rd pin connects, and the 8th pin meets VCC；
The 2nd of described multiplier U5,4,6 pins be all grounded, the 5th pin meets VEE, the 7th pin pass through resistance R7 and fortune
The 13rd pin calculating amplifier U3 connects, and the 8th pin meets VCC；
The 2nd of described multiplier U7,4,6 pins be all grounded, the 5th pin meets VEE, and the 7th pin connects multiplier U5's
1st pin, the 8th pin meets VCC；
Resistance R3=R5=R9=R10=R11=R12=R13=R14=R15=R16=10k Ω in circuit,
R25=R26=R27=R29=10k Ω, R7=R17=1K Ω, R28=5k Ω, R4=R6=100k Ω,
R1=R8=25K Ω, R18=R19=200K Ω, R2=50K Ω, electric capacity C1=C2=C3=10nF in circuit.
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| CN103414551B (en) * | 2013-08-02 | 2016-02-24 | 南京师范大学 | A kind of three-dimensional four wing chaos circuits |
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