Diversity of traveling wave solutions in FitzHugh–Nagumo type equations

doi:10.1016/j.jde.2009.03.023

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 期刊論文 > Item 987654321/50385

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題名:	Diversity of traveling wave solutions in FitzHugh–Nagumo type equations
作者:	Hsu, Cheng-hsiung;楊定揮;Yang, Ting-hui;Yang, Chi-ru
貢獻者:	淡江大學數學學系
日期:	2009-08
上傳時間:	2010-08-09 16:41:02 (UTC+8)
出版者:	Elsevier
摘要:	In this work we consider the diversity of traveling wave solutions of the FitzHugh–Nagumo type equations ut=uxx+ƒ(u, w), Wt=εg(u, w), where f(u,w)=u(u−a(w))(1−u) for some smooth function a(w) and g(u,w)=u−w. When a(w) crosses zero and one, the corresponding profile equation possesses special turning points which result in very rich dynamics. In [W. Liu, E. Van Vleck, Turning points and traveling waves in FitzHugh–Nagumo type equations, J. Differential Equations 225 (2006) 381–410], Liu and Van Vleck examined traveling waves whose slow orbits lie only on two portions of the slow manifold, and obtained the existence results by using the geometric singular perturbation theory. Based on the ideas of their work, we study the co-existence of different traveling waves whose slow orbits could involve all portions of the slow manifold. There are more complicated and richer dynamics of traveling waves than those of [W. Liu, E. Van Vleck, Turning points and traveling waves in FitzHugh–Nagumo type equations, J. Differential Equations 225 (2006) 381–410]. We give a complete classification of all different fronts of traveling waves, and provide an example to support our theoretical analysis.
關聯:	Journal of Differential Equations 247(4), pp.1185-1205
DOI:	10.1016/j.jde.2009.03.023
顯示於類別:	[數學學系暨研究所] 期刊論文

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