On Dynamics Analysis of a Novel Three-Dimensional Autonomous Chaotic System

Abstract:

This paper reports a novel three-dimensional autonomous chaotic system. By choosing an appropriate bifurcation parameter, we prove that a Hopf bifurcation occurs in this system when the bifurcation parameter exceeds a critical value, and some basic dynamical properties, such as Lyapunov exponents, fractal dimension, bifurcation diagram, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed numerical as well as theoretical analysis.

• Periodical: Applied Mechanics and Materials (Volumes 325-326)
• Pages: 228-232
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.325-326.228
• Online since: June 2013
• Authors: Wei Hong Jia
• Keywords: Bifurcation, Chaos, Lorenz System

References

[1] C. Sparrow, The Lorenz equations: Bifurcation, Chaos, and Strange Attractors, New York: Springer (1982)

[2] Guckenheimer J, Holmes P. Nonlinear oscillations, dynamical systems and bifurcation of vector field. New York: Springer (1983)

[3] Xiao bing Zhou ,Yue Wu ,Yi Li , Zhengxi Wei, Hopf bifurcation analysis of the Liu system. Chaos Solitons Fractals 36 (2008), p.1385

DOI: 10.1016/j.chaos.2006.09.008

[4] J. Lü, G. Chen and S. Zhang, Dynamical analysis of a new chaotic attractor. Int. J. Bifur. Chaos 12 (2002), p.1001

DOI: 10.1142/s0218127402004851

[5] J. Lü, Chen Guan rong, Zhang Suo chun. The compound structure of a new chaotic attractor. Chaos, Solitons and Fractals. 14 (2002), p.669

DOI: 10.1016/s0960-0779(02)00007-3

[6] Liu Chong, Liu Tao, Liu Ling, Liu Kai. A new chaotic attractor. Chaos, Solitons and Fractals 22 (2004), p.1031

DOI: 10.1016/j.chaos.2004.02.060