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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.

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
Full Text: DOI
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