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http://dx.doi.org/10.4134/BKMS.2014.51.2.457

HOPF BIFURCATION OF CODIMENSION ONE AND DYNAMICAL SIMULATION FOR A 3D AUTONOMOUS CHAOTIC SYSTEM  

Li, Xianyi (College of Mathematical Science Yangzhou University)
Zhou, Zhengxin (College of Mathematical Science Yangzhou University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.2, 2014 , pp. 457-478 More about this Journal
Abstract
In this paper, a 3D autonomous system, which has only stable or non-hyperbolic equilibria but still generates chaos, is presented. This system is topologically non-equivalent to the original Lorenz system and all Lorenz-type systems. This motivates us to further study some of its dynamical behaviors, such as the local stability of equilibrium points, the Lyapunov exponent, the dissipativity, the chaotic waveform in time domain, the continuous frequency spectrum, the Poincar$\acute{e}$ map and the forming mechanism for compound structure of its special cases. Especially, with the help of the Project Method, its Hopf bifurcation of codimension one is in detailed formulated. Numerical simulation results not only examine the corresponding theoretical analytical results, but also show that this system possesses abundant and complex dynamical properties not solved theoretically, which need further attention.
Keywords
3D autonomous system; chaos; Hopf bifurcation of codimension one; project method; Lyapunov exponent;
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