オガワ　トシユキ   OGAWA Toshiyuki   小川　知之    所属   明治大学  総合数理学部    職種   専任教授
言語種別	日本語
発行・発表の年月	2015/04
形態種別	学術雑誌
査読	査読あり
標題	Instability of periodic traveling wave solutions in a modified FitzHugh-Nagumo model for excitable media
執筆形態	共著(筆頭者以外)
掲載誌名	Applied Mathematics and Computation
掲載区分	国外
巻・号・頁	256,968-984頁
著者・共著者	M. Osman Gani, M. Osman Gani, Toshiyuki Ogawa
概要	We introduce a two-variable system of reaction-diffusion equations for excitable media. We numerically investigate the existence and stability of periodic traveling wave solutions in a two-dimensional parameter plane. Our results based on the method of continuation show a stability change of Eckhaus type. There are two families of periodic traveling waves: fast and slow. The fast family is stable in the case of standard FitzHugh-Nagumo excitable system. However, we observe that the fast family becomes unstable in our model. Consequently, it bifurcates to an oscillating wave. We explain this phenomenon by numerically calculating the essential spectra of the periodic traveling wave solutions. Moreover, we study the stability of the periodic traveling wave solutions for the Aliev-Panfilov excitable system and compare its results with the proposed model.
DOI	10.1016/j.amc.2015.01.109
ISSN	00963003
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