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2006•Journal of Qingdao UniversityRequires access

Chaos Controlling and Bifurcation of a Special Mathieu Function

Jiangang Zhang

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Abstract

The chaotic behaviors in a special mathieu function was analyzed by phase diagrams,Lyapunov exponent,Lyapunov dimension,Poincare map and global bifurcation graphs.Controlling the chaotic behaviors are based on the analysis.The chaotic behaviors in a special Mathieu function were controlled by means of the coupled feedback controlling method.By selecting proper controlling parameters according to bifurcation graph,the chaotic motions of the system can be successfully converted to the stable periodic orbits under coupled feedback controlling method.

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What this paper is about

The chaotic behaviors in a special mathieu function was analyzed by phase diagrams,Lyapunov exponent,Lyapunov dimension,Poincare map and global bifurcation graphs.Controlling the chaotic behaviors are based on the analysis.The chaotic behaviors in a special Mathieu function were controlled by means of the coupled feedback controlling method.By selecting proper controlling parameters according to bifurcation graph,the chaotic motions of the system can be successfully converted to the stable periodic orbits under coupled feedback controlling method.

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Available abstract

The chaotic behaviors in a special mathieu function was analyzed by phase diagrams,Lyapunov exponent,Lyapunov dimension,Poincare map and global bifurcation graphs.Controlling the chaotic behaviors are based on the analysis.The chaotic behaviors in a special Mathieu function were controlled by means of the coupled feedback controlling method.By selecting proper controlling parameters according to bifurcation graph,the chaotic motions of the system can be successfully converted to the stable periodic orbits under coupled feedback controlling method.

Key concepts: Lyapunov exponent, Chaotic, Bifurcation, Poincaré map, Mathematics, Bifurcation diagram, Mathieu function, Control theory (sociology)

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