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	2020/10
形態種別	学術雑誌
査読	査読あり
標題	Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka-Volterra system of three competing species
執筆形態	共著(筆頭者以外)
掲載誌名	Nonlinearity
掲載区分	国外
巻・号・頁	33(10),5080-5110頁
著者・共著者	Chueh Hsin Chang, Chiun Chuan Chen, Li Chang Hung, Masayasu Mimura, Toshiyuki Ogawa
概要	© 2020 IOP Publishing Ltd & London Mathematical Society. This paper considers the problem: if coexistence occurs in the long run when a third species w invades an ecosystem consisting of two species u and v on R, where u, v and w compete with one another. Under the assumption that the influence of w on u and v is small and other suitable conditions, we show that the three species can coexist as a non-monotone travelling wave. Such type of non-monotone waves plays an important role in the study of three-species phenomena. However, fewer results are known for the existence of such waves in the literature. Our approach, based on the method of sub-and super-solutions and bifurcation theory, provides a new approach to construct non-monotone waves of this type. Moreover, we show that the waves we construct are stable. To the best of our knowledge, this is the first rigorous result of stability for such type of waves.
DOI	10.1088/1361-6544/ab9244
ISSN	0951-7715