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BOUNDARY FEEDBACK ANTICONTROL OF SPATIOTEMPORAL CHAOS FOR 1D HYPERBOLIC DYNAMICAL SYSTEMS

YU HUANG

Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China

Supported in part by Natural Science Foundation of Guangdong Province, P. R. China.

https://doi.org/10.1142/S021812740401031XCited by:13 (Source: Crossref)

Abstract

In this paper, boundary anticontrol of spatiotemporal chaos for 1D hyperbolic equations is studied. Firstly, a new definition of chaotic vibrations for PDEs is given in terms of the growth rate of the total variations of the solutions with respect to the spatial variable as t→∞. Then, a boundary feedback controller is designed as composing with a sawtooth function, which can drive the originally nonchaotic linear or nonlinear dynamical system chaotic. Finally, as applications, anticontrol of chaos for 1D linear wave equations with linear or nonlinear boundary conditions is discussed.

Keywords:

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