Zhao Guangyu, Ruan Shigui
Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA.
J Math Pures Appl. 2011 Jun 1;96(6):627-671. doi: 10.1016/j.matpur.2010.11.005.
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().
我们研究了周期扩散的Lotka-Volterra竞争系统时间周期行波解的存在性、唯一性和渐近稳定性。在某些条件下，我们证明存在一个最大波速(c^)，使得对于每个波速(c\leq c^)，存在一个时间周期行波连接相应动力学系统的两个半平凡周期解。结果表明，这样的行波在平移意义下是唯一的，并且相对于其共动坐标系坐标是单调的。我们还表明，波速(c < c^)的行波解在某种意义下是渐近稳定的。此外，我们证明了对于非零波速(c > c^)不存在时间周期行波。
