Diversity of traveling wave solutions in FitzHugh–Nagumo type equations

doi:10.1016/j.jde.2009.03.023

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/50385

Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/50385

Title:	Diversity of traveling wave solutions in FitzHugh–Nagumo type equations
Authors:	Hsu, Cheng-hsiung;楊定揮;Yang, Ting-hui;Yang, Chi-ru
Contributors:	淡江大學數學學系
Date:	2009-08
Issue Date:	2010-08-09 16:41:02 (UTC+8)
Publisher:	Elsevier
Abstract:	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.
Relation:	Journal of Differential Equations 247(4), pp.1185-1205
DOI:	10.1016/j.jde.2009.03.023
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

Files in This Item:

File	Size	Format
0022-0396_247(4)p1185-1205.pdf	792Kb	Adobe PDF	272	View/Open
index.html	0Kb	HTML	175	View/Open
YJDEQ 5897.pdf	334Kb	Adobe PDF	146	View/Open

Loading...