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    題名: Snapback repellers and homoclinic orbits for multi-dimensional maps
    作者: Kang-Ling Liao;Chih-Wen Shih
    關鍵詞: Snapback repeller;Homoclinic orbit;Chaos
    日期: 2011-08-10
    上傳時間: 2017-10-25 02:10:49 (UTC+8)
    摘要: Marotto extended Li–Yorkeʼs 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 Marottoʼs 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.
    關聯: Journal of Mathematical Analysis and Applications, No. 386, 387-400.
    DOI: 10.1016/j.jmaa.2011.08.011
    顯示於類別:[數學學系暨研究所] 期刊論文


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