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Nonlinear Dynamics

, Volume 61, Issue 4, pp 707–715 | Cite as

Delayed feedback control and bifurcation analysis of Rossler chaotic system

  • Yuting Ding
  • Weihua Jiang
  • Hongbin Wang
Original paper

Abstract

In this paper, from the view of stability and chaos control, we investigate the Rossler chaotic system with delayed feedback. At first, we consider the stability of one of the fixed points, verifying that Hopf bifurcation occurs as delay crosses some critical values. Then, for determining the stability and direction of Hopf bifurcation we derive explicit formulae by using the normal-form theory and center manifold theorem. By designing appropriate feedback strength and delay, one of the unstable equilibria of the Rossler chaotic system can be controlled to be stable, or stable bifurcating periodic solutions occur at the neighborhood of the equilibrium. Finally, some numerical simulations are carried out to support the analytic results.

Keywords

Delayed feedback control Hopf bifurcation Chaos Rossler system 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina

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