Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems

It is a typical route to generate chaos via period-doubling bifurcations in some nonlinear systems. In this paper, 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. (C) 2003 Elsevier Science Ltd. All rights reserved.