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		Guogang LIU,Yi ZHAO.[en_title][J].Control Theory and Technology,2004,2(4):358~364.[Copy]

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GuogangLIU,YiZHAO
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Received:March 01, 2004Revised:October 10, 2004

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Chaotic vibration of the one-dimensional linear wave equation with a van der Pol nonlinear boundary condition

Guogang LIU, Yi ZHAO

(Department of Mathematics, Zhongshan University, Guangzhou Guangdong 510275, China)

Abstract:

The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations. It characterizes the nonisotropic chaotic vibration by means of the total variation theory. Some results are derived on the exponential growth of total variation of the snapshots on the spatial interval in the long-time horizon when the map and the initial condition satisfy some conditions.

Key words: Chaos Wave equation Van der Pol nonlinearity Total variation Homoclinic point Topological transitivity.