Title: Snapback repellers and homoclinic orbits for multi-dimensional maps
Authors: Liao, Kang-Ling
Shih, Chih-Wen
Department of Applied Mathematics
Keywords: Snapback repeller;Homoclinic orbit;Chaos
Issue Date: 1-Feb-2012
Abstract: Marotto extended Li-Yorke's theorem on chaos from one-dimension to multi-dimension through introducing the notion of snapback repeller in 1978. Due to a technical flaw, he redefined snapback repeller in 2005 to validate this theorem. This presentation provides two methodologies to facilitate the application of Marotto's theorem. The first one is to estimate the radius of repelling neighborhood for a repelling fixed point. This estimation is of essential and practical significance as combined with numerical computations of snapback points. Secondly, we propose a sequential graphic-iteration scheme to construct homoclinic orbit for a repeller. This construction allows us to track the homoclinic orbit. Applications of the present methodologies with numerical computation to a chaotic neural network and a predator-prey model are demonstrated. (C) 2011 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jmaa.2011.08.011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.08.011
Volume: 386
Issue: 1
Begin Page: 387
End Page: 400
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