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Chaotic control and bifurcation analysis of a third-order chaotic system. (Chinese. English summary) Zbl 1340.37059

Summary: From the view of stability and chaos control, the effect of delay on the dynamics of a three order chaotic system with delayed feedback is investigated. Firstly, the effect of delay on the equilibrium points and the existence of local Hopf bifurcation are considered. Secondly, by using the center manifold theory and normal form method, the explicit formulas determining the stability and direction of bifurcating periodic solutions are derived. By designing appropriate feedback strength and delay, chaotic oscillation is converted into a stable equilibrium or a stable periodic orbit. Finally, some numerical simulations are carried out to support the analytic results.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems
37L15 Stability problems for infinite-dimensional dissipative dynamical systems
93B52 Feedback control