Delayed feedback control and bifurcation analysis of Rossler chaotic system |
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Authors: | Yuting Ding Weihua Jiang Hongbin Wang |
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Institution: | (1) College of Mathematics, Jilin University, 10 Qian Wei Road, Changchun, 130012, P.R. China;(2) Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. China |
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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. |
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