Analysis of chaotic saddles in high-dimensional dynamical systems: the Kuramoto-Sivashinsky equation |
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Authors: | Rempel Erico L Chian Abraham C-L Macau Elbert E N Rosa Reinaldo R |
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Institution: | National Institute for Space Research (INPE), P. O. Box 515, 12227-010 Sao Jose dos Campos-SP, Brazil. |
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Abstract: | This paper presents a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems. Our methodology is applied to the Kuramoto-Sivashinsky equation, a reaction-diffusion partial differential equation. The paper describes a novel technique that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a chaotic attractor. The numerical techniques explained here are important to improve the understanding of the connection between low-dimensional chaotic systems and spatiotemporal systems which exhibit temporal chaos and spatial coherence. |
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