Hopf bifurcation analysis of the Liu system

Xiaobing Zhou, Yue Wu, Yi Li and Zhengxi Wei

Chaos, Solitons & Fractals, 2008, vol. 36, issue 5, 1385-1391

Abstract: In this paper, a three dimensional autonomous system which is similar to the Lorenz system is considered. By choosing an appropriate bifurcation parameter, we prove that a Hopf bifurcation occurs in this system when the bifurcation parameter exceeds a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is presented by applying the normal form theory. Finally, an example is given and numerical simulations are performed to illustrate the obtained results.

Date: 2008
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:36:y:2008:i:5:p:1385-1391

DOI: 10.1016/j.chaos.2006.09.008

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