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A unique signum switch for chaos
and hyperchaos
Chunbiao Li, Julien Clinton Sprott
Wesley Thio, Huanqiang Zhu
Email: [email protected]
[email protected]
Acknowledgement --- Cooperators
 Julien Clinton Sprott
 Wesley Thio
 Huanqiang Zhu
Acknowledgement
 This work was supported financially by the Jiangsu Overseas
Research and Training Program for University Prominent
Young and Middle-aged Teachers and Presidents, the 4th 333
High-level Personnel Training Project (Su Talent [2011]
No.15) and the National Science Foundation for Postdoctoral
General Program and Special Founding Program of People’s
Republic of China (Grant No. 2011M500838 and Grant No.
2012T50456) and Postdoctoral Research Foundation of
Jiangsu Province (Grant No. 1002004C).
A Unique Circuit Switch for ASIG(B)
 Traditional Method
x
+
+
y
z
sgn(x)
+
+
zsgn(x)
-x
sgn(y)
-xsgn(y)
New Circuit Element
Signal Line
R16
D1
R17
D2
-z
R18
D3
+ U9
R20
R21
+U11
D4
R19
z
-zsgn(x) zsgn(x)
D5 D6 D7
D8
x
+U10
Control Line
Signal Line
x
-x
R22
D9
R23
D10
R24
D11
R26
R27
+U14
D12
R25
+U12
xsgn(y) -xsgn(y)
D13 D14 D15 D16
y
+U13
Control Line
 x  y  x,
 y   z sgn( x)  u ,


 z  x sgn( y )  a,
u  by,
Lyapunov exponents of system
versus b at a = 1
(a)
(b)
Hyperchaotic attractor with initial conditions (1, 0, 3, 0) (a) x-y phase
plane, (b) x-z phase plane, (c) y-z phase plane, (d) x-u phase plane
when b = 0.1
Projection onto the x-y plane of a cross-section of the attractor
at z = 0
 x  y  x,

 y   z sgn( x ),
 z  x sgn( y )  a,

x
-y
-u
zsgn(x)
V+
-xsgn(y)
y
C1
R1
x
R3
R4
-x
R2
+ U2
+ U1
R5
C2
y
R7
R8
-y
R6
R9
+ U3
C3
+ U4
z
R11
R12
-z
R10
R13
+ U5
C4
+ U7
+ U6
u
R14
R15
-u
+ U8
Four integration channels in circuit structure for
the 4-D system
Oscilloscope traces of hyperchaotic attractors (a) x-y plane, (b)
x-z plane, (c) y-z plane, (d) x-u plane (1V/div).
Experimental phase portraits of 3-D chaotic system (a) x-y
plane, (b) x-z plane, (c) y-z plane (1V/div).
Thanks