2010•Zenodo (CERN European Organization for Nuclear Research)Open access

Hopf Bifurcation For A New Chaotic System

Kejun Zhuang

Abstract

In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.

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Available abstract

Key concepts: Chaotic, Bogdanov–Takens bifurcation, Hopf bifurcation, Bifurcation, Mathematics, Pitchfork bifurcation, Applied mathematics, Environmental science