標題: Snapback repellers and homoclinic orbits for multi-dimensional maps
作者: Liao, Kang-Ling
Shih, Chih-Wen
應用數學系
Department of Applied Mathematics
關鍵字: Snapback repeller;Homoclinic orbit;Chaos
公開日期: 1-二月-2012
摘要: 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
http://hdl.handle.net/11536/14878
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.08.011
期刊: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume: 386
Issue: 1
起始頁: 387
結束頁: 400
顯示於類別:期刊論文


文件中的檔案:

  1. 000295563300034.pdf