Analysis and Control of Chaos for a Sort of Mathieu Equation

By means of numerical simulations,the bifurcation and the chaotic behaviors of a nonlinear Mathieu function are studied.The route to chaos is revealed by global bifurcation diagram.Phase portraits,bifurcation diagram and Lyapunov-exponent spectrum are also presented to analyze nonlinear dynamics of the system.The method,which is a subsection square function,is adopted as the nonlinear feedback controller to control chaos in this paper.By selecting proper controlling parameters according to bifurcation diagrams,the chaotic motions of the system can be successfully converted to different stable periodic orbits.The results are demonstrated and illustrated by reverse periodic-doubling bifurcation diagrams and phase portraits.