Bifurcation analysis of Rössler system with multiple delayed feedback
Meihong Xu, Harbin Institute of Technology Harbin, P. R. China E. J. Qualitative Theory of Diff. Equ., No. 63. (2010), pp. 1-22.
Yuan Wei, Beijing Institute of Strength and Environment, Beijing, P. R. China
Junjie Wei, Harbin Institute of Technology Harbin, P. R. China
| Communicated by Bo Zhang. | Received on 2010-02-10 Appeared on 2010-10-01 |
Abstract: In this paper, regarding the delay as parameter, we investigate the effect of delay on the dynamics of a Rössler system with multiple delayed feedback proposed by Ghosh and Chowdhury. At first we consider the stability of equilibrium and the existence of Hopf bifurcations. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, we give a numerical simulation example which indicates that chaotic oscillation is converted into a stable steady state or a stable periodic orbit when the delay passes through certain critical values.
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