標題: Diversity of traveling wave solutions in FitzHugh-Nagumo type equations
作者: Hsu, Cheng-Hsiung
Yang, Ting-Hui
Yang, Chi-Ru
應用數學系
Department of Applied Mathematics
公開日期: 15-八月-2009
摘要: In this work we consider the diversity of traveling wave solutions of the FitzHugh-Nagumo type equations u(t) = u(xx) + f (u, w), w(t) = epsilon g(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. (C) 2009 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jde.2009.03.023
http://hdl.handle.net/11536/6815
ISSN: 0022-0396
DOI: 10.1016/j.jde.2009.03.023
期刊: JOURNAL OF DIFFERENTIAL EQUATIONS
Volume: 247
Issue: 4
起始頁: 1185
結束頁: 1205
顯示於類別:期刊論文


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