Traveling wave front for a two-component lattice dynamical system arising in competition models.
Dr. Chang Hong WuOhio State University, USA 下午 2:00–3:00 鴻經館 107 室We study traveling wave front solutions for a two-component system on a one-dimensional lattice. This system arises in the study of the competition between two species with diffusion (or migration), if we divide the habitat into discrete regions or niches. We consider the case when the nonlinear source terms are of Lotka-Volterra type. For the monostable case, we first show that there is a minimal wave speed such that a traveling wave front exists if and only if its speed is above this minimal wave speed. Next, we characterize the minimal wave speed using the parameters in the system. Then we show that any wave profile is strictly monotone. Moreover, under some conditions, we show that the wave profile is unique (up to translations) for a given wave speed. Finally, for the numerical aspect, we derive the convergence of discretized minimal wave speeds as the mesh size tends to zero.