Hopf Bifurcation Analysis and Anticontrol of Hopf Circles of the Rössler-Like System | Zendy

Ranchao Wu | Zendy; Xiang Li | Zendy

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Hopf Bifurcation Analysis and Anticontrol of Hopf Circles of the Rössler-Like System

Author(s) -

Ranchao Wu,

Xiang Li

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/341870

Subject(s) - hopf bifurcation , mathematics , attractor , scheme (mathematics) , synchronization (alternating current) , control theory (sociology) , bifurcation , pure mathematics , mathematical analysis , topology (electrical circuits) , computer science , combinatorics , control (management) , nonlinear system , physics , quantum mechanics , artificial intelligence

A new Rössler-like system is constructed by the linear feedback control scheme in this paper. As well, it exhibits complex dynamical behaviors, such as bifurcation, chaos, and strange attractor. By virtue of the normal form theory, its Hopf bifurcation and stability are investigated in detail. Consequently, the stable periodic orbits are bifurcated. Furthermore, the anticontrol of Hopf circles is achieved between the new Rössler-like system and the original Rössler one via a modified projective synchronization scheme. As a result, a stable Hopf circle is created in the controlled Rössler system. The corresponding numerical simulations are presented, which agree with the theoretical analysis

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