The paper mainly focuses on a novel hyperchaotic system. The local stability of equilibrium is analyzed and existence of Hopf bifurcation is established. Moreover, formulas for determining the stability and direction of bifurcating periodic solutions are derived by center manifold theorem and normal form theory. Finally, numerical simulation is given to illustrate the theoretical analysis.

References

References
1.
Chen
,
G.
, and
Ueta
,
T.
,
1999
, “
Yet Another Chaotic Attractor
,”
Int. J. Bifur. Chaos
,
9
, pp.
1465
1466
.10.1142/S0218127499001024
2.
,
J.
, and
Chen
,
G.
,
2002
, “
A New Chaotic Attractor Coined.
Int. J. Bifur. Chaos
,
12
, pp.
659
661
.10.1142/S0218127402004620
3.
Liu
,
C.
,
Liu
,
T.
,
Liu
,
L.
, and
Liu
,
K.
,
2004
, “
A New Chaotic Attractor
,”
Chaos Solitons Fractals
,
22
, pp.
1031
1038
.10.1016/j.chaos.2004.02.060
4.
Qi
,
G.
,
Chen
,
G.
,
Du
,
S.
,
Chen
,
Z.
, and
Yuan
,
Z.
,
2005
, “
Analysis of a New Chaotic System
,”
Physica A
,
352
, pp.
295
308
.10.1016/j.physa.2004.12.040
5.
Tigan
,
G.
,
2008
, “
Analysis of a 3D Chaotic System
,”
Chaos Solitons Fractals
,
36
, pp.
1315
1319
.10.1016/j.chaos.2006.07.052
6.
Zhu
,
C.
,
2012
, “
A Novel Image Encryption Scheme Based on Improved Hyperchaotic Sequences
,”
Opt. Commun.
,
285
, pp.
29
37
.10.1016/j.optcom.2011.08.079
7.
Smaoui
,
N.
,
Karouma
,
A.
, and
Zribi
,
M.
,
2011
, “
Secure Communications Based on the Synchronization of the Hyperchaotic Chen and the Unified Chaotic Systems
,”
Commun. Nonlinear Sci. Numer. Simulat.
,
16
, pp.
3279
3293
.10.1016/j.cnsns.2010.10.023
8.
Liu
,
M.
,
Peng
,
J.
, and
Tse
,
C. K.
,
2010
, “
A New Hyperchaotic System and Its Circuit Implementation
,”
Int. J. Bifur. Chaos
,
20
, pp.
1201
1208
.10.1142/S021812741002640X
9.
Wang
,
X.
, and
Wang
,
M.
,
2008
, “
A Hyperchaos Generated From Lorenz System
,”
Physica A
,
387
, pp.
3751
3758
.10.1016/j.physa.2008.02.020
10.
Niu
,
Y.
,
Wang
,
X.
,
Wang
,
M.
, and
Zhang
,
H.
,
2010
, “
A New Hyperchaotic System and Its Circuit Impliementation
,”
Commun. Nonlinear Sci. Numer. Simulat.
,
15
, pp.
3518
3524
.10.1016/j.cnsns.2009.08.014
11.
Liu
,
M.
, and
Feng
,
J.
,
2009
, “
A New Hyperchaotic System
,”
Acta Phys. Sin.
,
58
, pp.
4457
4462
(in Chinese)
.
12.
Wu
,
Y.
,
Zhou
,
X.
,
Chen
,
J.
, and
Hui
,
B.
,
2009
, “
Chaos Synchronization of a New 3D Chaotic System
,”
Chaos Solitons Fractals
,
42
, pp.
1812
1819
.10.1016/j.chaos.2009.03.092
13.
Tao
,
C.
,
Yang
,
C.
,
Luo
,
Y.
,
Xiang
,
H.
, and
Hu
,
F.
,
2005
, “
Speed Feedback Control of Chaotic System
,”
Chaos Solitons Fractals
,
23
, pp.
259
263
.10.1016/j.chaos.2004.04.009
14.
Yu
,
W.
,
2010
, “
Stabilization of Three-Dimensional Chaotic Systems Via Single State Feedback Controller
,”
Phys. Lett. A
,
374
, pp.
1488
1492
.10.1016/j.physleta.2010.01.048
15.
Yan
,
Z.
,
2005
, “
Controlling Hyperchaos in the New Hyperchaotic Chen System
,”
Appl. Math. Comput.
,
168
, pp.
1239
1250
.10.1016/j.amc.2004.10.016
16.
Tao
,
C.
, and
Liu
,
X.
,
2007
, “
Feedback and Adaptive Control and Synchronization of a Set of Chaotic and Hyperchaotic Systems
,”
Chaos Solitons Fractals
,
32
, pp.
1572
1581
.10.1016/j.chaos.2005.12.005
17.
Laoye
,
J. A.
,
Vincent
,
U. E.
, and
Kareem
,
S. O.
,
2009
, “
Chaos Control of 4D Chaotic Systems Using Recursive Backstepping Nonlinear Controller
,”
Chaos Solitons Fractals
,
39
, pp.
356
362
.10.1016/j.chaos.2007.04.020
18.
Wei
,
Z.
, and
Yang
,
Q.
,
2010
, “
Anti-Control of Hopf Bifurcation in the New Chaotic System With Two Stable Node-Foci
,”
Appl. Math. Comput.
,
217
, pp.
422
429
.10.1016/j.amc.2010.05.035
19.
Mello
,
L. F.
,
Messias
,
M.
, and
Braga
,
D. C.
,
2008
, “
Bifurcation Analysis of a New Lorenz-Like Chaotic System
,”
Chaos Solitons Fractals
,
37
, pp.
1244
1255
.10.1016/j.chaos.2007.11.008
20.
Mittal
,
A. K.
,
Mukherjee
,
S.
, and
Shukla
,
R. P.
,
2011
, “
Bifurcation Analysis of Some Forced Lü Systems
,”
Commun. Nonlinear Sci. Numer. Simulat.
,
16
, pp.
787
797
.10.1016/j.cnsns.2010.04.016
21.
Zhuang
,
K.
,
2010
, “
Hopf Bifurcation for a New Chaotic System
,”
Int. J. Comput. Math. Sci.
,
4
, pp.
354
357
.
22.
Zhang
,
K.
, and
Yang
,
Q.
,
2010
, “
Hopf Bifurcation Analysis in a 4D-Hyperchaotic System
,”
J. Syst. Sci. Complex
,
23
, pp.
748
758
.10.1007/s11424-010-8084-y
23.
Yang
,
Q.
, and
Chen
,
G.
,
2008
, “
A Chaotic System With One Saddle and Two Stable Node-Foci
,”
Int. J. Bifur. Chaos
,
18
, pp.
1393
1414
.10.1142/S0218127408021063
24.
Hassard
,
B. D.
,
Kazarinoff
,
N. D.
, and
Wan
,
Y. H.
,
1981
,
Theory and Applications of Hopf Bifurcation
,
1st ed.
,
Cambridge University Press
,
Cambridge
.
You do not currently have access to this content.