IJPAM: Volume 104, No. 1 (2015)

HOPF BIFURCATION ANALYSIS OF ZHOU SYSTEM

Tee Loong Soon$^1$, Zabidin Salleh$^2$
$^1$HELP Matriculation Centre
HELP University
Kompleks Pejabat Damansara (KPD), Jalan Dungun,
50490, Kuala Lumpur, MALAYSIA
$^2$School of Informatics and Applied Mathematics
Universiti Malaysia Terengganu
21030, Kuala Terengganu, Terengganu, MALAYSIA


Abstract. In this paper, we conducted an extension research from [#!19!#] which was mainly on studying the dynamical behaviour such as Lyapunov exponents, bifurcation diagram, etc. of a chaotic attractor namely Zhou System. In order to understand the Zhou system more depth, we presented the analysis of the system by using Complementary-Cluster Energy-Barrier Criterion (CCEBC) and Routh-Hurwitz Criterion. Besides that, we have demonstrated the occurrence of Hopf bifurcation. The results showed that the Zhou system undergoes a supercritical Hopf bifurcation under a special condition by means of the first Lyapunov coefficient.

Received: March 19, 2015

AMS Subject Classification: 34C23, 34C28, 37M20

Key Words and Phrases: dynamical system, chaos, Zhou system, Hopf bifurcation

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DOI: 10.12732/ijpam.v104i1.1 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 1
Pages: 1 - 18


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