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.