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Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems. (English) Zbl 1073.37512
Summary: It is a typical route to generate chaos via period-doubling bifurcations in some nonlinear systems. We propose a new hybrid control strategy in which state feedback and parameter perturbation are used to control the period-doubling bifurcations and to stabilize unstable periodic orbits embedded in the chaotic attractor of a discrete chaotic dynamical system. Simulation shows that the higher stable \(2^n\)-periodic orbit of the system can be controlled to lower stable \(2^m\)-periodic orbits, \(m<n\), by this methods. Some other numerical simulations are also presented to verify the theoretical analysis.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C10 Nonlinear systems in control theory
93B52 Feedback control
37C27 Periodic orbits of vector fields and flows
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