|
|||||
|
|
Topological Horseshoes of Traveling Waves for a Fast–Slow Predator–Prey System |
|
| Authors: | Marcio Gameiro Tomáš Gedeon William Kalies Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka |
| Affiliation: | (1) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA;(2) Department of Mathematical Sciences, Montana State University, Bozeman, MA 59717, USA;(3) Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA;(4) Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan;(5) Department of Applied Mathematics and Informatics, Ryukoku University, Seta Otsu, 520-2194, Japan |
| Abstract: | We show the existence of a set of periodic traveling waves in a system of two scalar reaction diffusion equations, which is in one-to-one correspondence with a full shift on two symbols. We use a novel combination of rigorous numerical computations and the topological techniques of the Conley index theory. This approach is quite general, and this paper is intended as a demonstration of its usefulness and applicability. |
| Keywords: | Singular perturbation Conley index theory traveling wave symbolic dynamics rigorous computation predator– prey system |
| 本文献已被 SpringerLink 等数据库收录！ | |