Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka–Volterra competition system with diffusion
✍ Scribed by Guangyu Zhao; Shigui Ruan
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 469 KB
- Volume
- 95
- Category
- Article
- ISSN
- 0021-7824
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✦ Synopsis
We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c(*) such that for each wave speed c ≤ c(*), there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c < c(*) are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves for nonzero speed c > c(*).