2006•Journal of Xi'an University of TechnologyRequires access

Chaos Controlling for a Kind of Mathieu Equation

Xu Huidong, Jiangang Zhang

Abstract

The numerical method is used to reveal the bifurcations and chaotic behaviors in nonlinear mathieu equation.The route to chaos is revealed by global bifurcation graph.Phase diagrams,time response and Lyapunov exponents are presented to analyse dynamic behavior of system.The proper controlling parameter can be selected via the bifurcation graph.The chaotic behaviors in the system can be effectively controlled to the different periodic orbits using the coupling feedback controlling and x｜x｜controlling methods.

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Key concepts: Bifurcation, Lyapunov exponent, Chaotic, Mathieu function, Nonlinear system, Bifurcation diagram, Graph, Control theory (sociology)