Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function | Zendy

Jiangang Zhang | Zendy; Yan-Dong Chu | Zendy; Wenju Du | Zendy; Chang Ying-xiang | Zendy; Xinlei An | Zendy

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Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function

Author(s) -

Jiangang Zhang,

Yan-Dong Chu,

Wenju Du,

Chang Ying-xiang,

Xinlei An

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/371509

Subject(s) - chaotic , quantum entanglement , synchronization of chaos , control theory (sociology) , hopf bifurcation , bifurcation , chaotic hysteresis , mathematics , function (biology) , equilibrium point , chaos (operating system) , control of chaos , stability (learning theory) , statistical physics , computer science , mathematical analysis , physics , nonlinear system , quantum , quantum mechanics , control (management) , differential equation , artificial intelligence , computer security , evolutionary biology , biology , machine learning

A new approach to generate chaotic phenomenon, called chaos entanglement, is introduced in this paper. The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner. The Hopf bifurcation of a new chaotic system with chaos entanglement function is studied. More precisely, we study the stability and bifurcations of equilibrium in the new chaotic system. Besides, we controlled the system to any fixed point to eliminate the chaotic vibration by means of sliding mode method. And the numerical simulations were presented to confirm the effectiveness of the controller

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