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Abstract and Applied Analysis
Volume 2012, Article ID 341870, 16 pages
http://dx.doi.org/10.1155/2012/341870
Research Article

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

School of Mathematics, Anhui University, Hefei 230039, China

Received 15 March 2012; Accepted 20 June 2012

Academic Editor: Allan Peterson

Copyright © 2012 Ranchao Wu and Xiang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.