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INVARIANT MANIFOLD WITH COMPLETE FOLIATIONS AND CHAOTIFICATION ANALYSIS FOR A KIND OF PDES WITH BOUNDARY COUPLING

LINGLI XIE

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

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KOK-LAY TEO

Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia

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, and

YI ZHAO

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

Author for correspondence.

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https://doi.org/10.1142/S0218127407018944Cited by:0 (Source: Crossref)

Abstract

In this paper, we are concerned with the existence of invariant manifolds and complete foliations for a class of PDEs with boundary coupling. Some new form of gap relative coupling and inequality conditions are obtained. Further, we prove the topological equivalence of the flows in the respective attractors between the system and its spatial discretization system (an ODE system). Finally, the chaotification of the system is discussed through an example and simulation is generated to illustrate the theoretical results.

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