Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30840
Hopf Bifurcation for a New Chaotic System

Authors: Kejun Zhuang


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.

Keywords: Hopf Bifurcation, chaotic system, normal form theory

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1153


[1] E.N. Lorenz. Deterministic non-periodic flows. J. Atmospheric. Sci. 20 (1963), 130-141.
[2] Q.E. R¨ossler. An equation for continuous chaos. Phys. Lett. A 57 (1976), 397-398.
[3] G. Chen, T. Ueta. Yet another chaotic attractor. Int. J. Bifur. Chaos 9 (1999), 1465-1466.
[4] J. L¨u, G. Chen. A new chaotic attractor coined. Int. J. Bifur. Chaos 12 (2002), 659-661.
[5] C. Liu, T. Liu, L. Liu, K. Liu. A new chaotic attractor. Chaos, Solitons and Fractals 22 (2004), 1031-1038.
[6] G. Qi, G. Chen, S. Du, Z. Chen, Z. Yuan. Analysis of a new chaotic system. Physica A 352 (2005), 295-308.
[7] G. Tigan. Analysis of a 3D chaotic system. Chaos, Solitons and Fractals 36 (2008), 1315-1319.
[8] J. Wang, Z. Chen, Z. Yuan. A new chaotic system and analysis of its properties. Acta Physica Sinica 55 (2006), 3956-3963. (in Chinese)
[9] J. Wang, Z. Chen, Z. Yuan. Existence of a new three-dimensional chaotic attractor. Chaos, Solitons and Fractals 42 (2009), 3053-3057.
[10] B.D. Hassard, N.D. Kazarinoff, Y.H. Wan. Theory and Applications of Hopf bifurcation. Cambridge: Cambridge University Press, 1981.