Traveling wave solutions in temporally discrete reaction-diffusion systems with delays

摘要

An idea used by W. Li et al. (Nonlinearity 19, 1253-73, 2006) is extended to show existence of traveling wave solutions for a class of temporally discrete reaction-diffusion systems with delays. The result is an generalization of an existing result for scalar equations to systems. As examples, the obtained abstract results will be applied to temporally discrete diffusion-competition systems with delay. Our results suggest temporally discrete diffusion-competition systems are dynamically consistent with the differential diffusion-competition systems. An idea used by W. Li et al. (Nonlinearity 19, 1253-1273, 2006) is extended to show existence of traveling wave solutions for a class of temporally discrete reaction-diffusion systems with delays. The result is a generalization of an existing result for scalar equations to systems. As examples, the obtained abstract results will be applied to temporally discrete diffusion- competition systems with delay. The results suggest temporally discrete diffusion-competition systems are dynamically consistent with the differential diffusion-competition systems.