It is very important to generate hyperchaos with more complicated dynamics as a model for theoretical research and practical application. A new hyperchaotic system with double piecewise-linear functions in state equations is presented and physically implemented by circuit design. Based on the theoretical analyses and simulations, the hyperchaotic dynamical properties of this nonlinear system are revealed by equilibria, Lyapunov exponents, and bifurcations, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.

References

References
1.
Matsumoto
,
T.
,
Chua
,
L. O.
, and
Kobayashi
,
K.
,
1986
, “
Hyperchaos: Laboratory Experiment and Numerical Confirmation
,”
IEEE Trans. Circuits Syst.
,
33
(
11
), pp.
1143
1147
.10.1109/TCS.1986.1085862
2.
Mahmoud
,
G. M.
,
Mahmoud
,
E. E.
, and
Arafa
,
A. A.
,
2013
, “
Controlling Hyperchaotic Complex Systems With Unknown Parameters Based on Adaptive Passive Method
,”
Chin. Phys. B.
,
22
(
6
), p.
060508
.10.1088/1674-1056/22/6/060508
3.
Wang
,
Z. S.
, and
Zhang
,
H. G.
,
2013
, “
Synchronization Stability in Complex Interconnected Neural Networks With Nonsymmetric Coupling
,”
Neurocomputing
,
108
(5), pp.
84
92
.10.1016/j.neucom.2012.11.014
4.
Wang
,
H.
,
Han
,
Z. Z.
,
Xie
,
Q. Y.
, and
Zhang
,
W.
,
2009
, “
Finite-Time Chaos Synchronization of Unified Chaotic System With Uncertain Parameters
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
(
5
), pp.
2239
2247
.10.1016/j.cnsns.2008.04.015
5.
Zhang
,
Y. Q.
, and
Wang
,
X. Y.
,
2014
, “
A Symmetric Image Encryption Algorithm Based on Mixed Linear–Nonlinear Coupled Map Lattice
,”
Inf. Sci.
,
273
(7), pp.
329
351
.10.1016/j.ins.2014.02.156
6.
Liu
,
H. J.
,
Wang
,
X. Y.
, and
Zhu
,
Q. L.
,
2011
, “
Asynchronous Anti-Noise Hyper Chaotic Secure Communication System Based on Dynamic Delay and State Variables Switching
,”
Phys. Lett. A
,
375
(
30–31
), pp.
2828
2835
.10.1016/j.physleta.2011.06.029
7.
Wang
,
X.
, and
Chen
,
G. R.
,
2013
, “
Constructing a Chaotic System With Any Number of Equilibria
,”
Nonlinear Dyn.
,
71
(
3
), pp.
429
436
.10.1007/s11071-012-0669-7
8.
Zheng
,
S.
,
Dong
,
G. G.
, and
Bi
,
Q. S.
,
2010
, “
A New Hyperchaotic System and Its Synchronization
,”
Appl. Math. Comput.
,
215
(
9
), pp.
3192
3200
.10.1016/j.amc.2009.09.060
9.
Liu
,
W. B.
,
Tang
,
W. K. S.
, and
Chen
,
G. R.
,
2011
, “
Forming and Implementing a Hyperchaotic System With Rich Dynamics
,”
Chin. Phys. B.
,
20
(
9
), p.
090510
.10.1088/1674-1056/20/9/090510
10.
Han
,
Q.
,
Liu
,
C. X.
,
Sun
,
L.
, and
Zhu
,
D. R.
,
2013
, “
A Fractional Order Hyperchaotic System Derived From a Liu System and Its Circuit Realization
,”
Chin. Phys. B.
,
22
(
2
), p.
020502
.10.1088/1674-1056/22/2/020502
11.
Rössler
,
O. E.
,
1979
, “
An Equation for Hyperchaos
,”
Phys. Lett. A.
,
71
(
2,3
), pp.
155
157
.10.1016/0375-9601(79)90150-6
12.
Wang
,
X. Y.
, and
Wang
,
M. J.
,
2007
, “
Hyperchaotic Lorenz System
,”
Acta Phys. Sin.
,
56
(
9
), pp.
5136
5141
. Available at: http://wulixb.iphy.ac.cn/CN/volumn/home.shtml
13.
Qi
,
G. Y.
,
Du
,
S. Z.
,
Chen
,
G. R.
,
Chen
,
Z. Q.
, and
Yuan
,
Z. Z.
,
2005
, “
On a Four-Dimensional Chaotic System
,”
Chaos, Solitons Fractals
,
23
(
5
), pp.
1671
1682
.10.1016/j.chaos.2004.06.054
14.
Saito
,
T.
,
1990
, “
An Approach Toward Higher Dimensional Hysteresis Chaos Generator
,”
IEEE Trans. Circuits Syst.
,
37
(
3
), pp.
399
409
.10.1109/31.52733
15.
Yu
,
S. M.
,
,
J. H.
, and
Chen
,
G. R.
,
2007
, “
A Family of n-Scroll Hyperchaotic Attractors and Their Realization
,”
Phys. Lett. A
,
364
(
3–4
), pp.
244
251
.10.1016/j.physleta.2006.12.029
16.
Yalcin
,
M. E.
,
Suykens
,
J. A. K.
, and
Vandewalle
,
J. P. L.
,
2005
,
Cellular Neural Networks, Multi-Scroll Chaos and Synchronization
,
World Scientific
,
Singapore
, Chap. 4.
17.
,
J. H.
, and
Chen
,
G. R.
,
2006
, “
Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications
,”
Int. J. Bifurc. Chaos.
,
16
(
4
), pp.
775
858
.10.1142/S0218127406015179
18.
Zhang
,
Y. Q.
, and
Wang
,
X. Y.
,
2014
, “
Spatiotemporal Chaos in Mixed Linear–Nonlinear Coupled Logistic Map Lattice
,”
Physica A
,
402
(5), pp.
104
118
.10.1016/j.physa.2014.01.051
19.
Zhang
,
Y. Q.
, and
Wang
,
X. Y.
,
2013
, “
Spatiotemporal Chaos in Arnold Coupled Logistic Map Lattice
,”
Nonlinear Anal. Model. Control
,
18
(
4
), pp.
526
541
. Available at: http://www.mii.lt/NA/
20.
Teng
,
L.
,
Iu
,
H. H. C.
,
Wang
,
X. Y.
, and
Wang
,
X. K.
,
2014
, “
Chaotic Behavior in Fractional-Order Memristor-Based Simplest Chaotic Circuit Using Fourth Degree Polynomial
,”
Nonlinear Dyn.
,
77
(
1–2
), pp.
231
241
.10.1007/s11071-014-1286-4
21.
Fitch
,
A. L.
,
Yu
,
D.
,
Iu
,
H. H. C.
, and
Sreeram
,
V.
,
2012
, “
Hyperchaos in a Memristor-Based Modified Canonical Chua's Circuit
,”
Int. J. Bifurc. Chaos
,
22
(
6
), p.
1250133
.10.1142/S0218127412501337
22.
Niu
,
Y. J.
,
Wang
,
X. Y.
,
Wang
,
M. J.
, and
Zhang
,
H. G.
,
2010
, “
A New Hyperchaotic System and Its Circuit Implementation
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
11
), pp.
3518
3524
.10.1016/j.cnsns.2009.08.014
23.
Wang
,
X. Y.
, and
Wang
,
M. J.
,
2008
, “
A Hyperchaos Generated From Lorenz System
,”
Physica A
,
387
(
14
), pp.
3751
3758
.10.1016/j.physa.2008.02.020
24.
Barboza
,
R.
,
2008
, “
Hyperchaos in a Chua's Circuit With Two New Added Branches
,”
Int. J. Bifurc. Chaos.
,
18
(
4
), pp.
1151
1159
.10.1142/S0218127408020884
25.
Matsumoto
,
T.
,
Chua
,
L. O.
, and
Komuro
,
M.
,
1985
, “
The Double Scroll
,”
IEEE Trans. Circuits Syst.
,
32
(
8
), pp.
798
818
.10.1109/TCS.1985.1085791
26.
Wolf
,
A.
,
Swift
,
J. B.
,
Swinney
,
H. L.
, and
Vastano
,
J. A.
,
1985
, “
Determining Lyapunov Exponents From a Time Series
,”
Physica D
,
16
(
3
), pp.
285
317
.10.1016/0167-2789(85)90011-9
You do not currently have access to this content.