Asymptotic periodicity and permanence in a competition-diffusion system with discrete delays

摘要

We study a class of reaction-diffusion systems modeling the dynamics of two competing species with T-periodic environmental parameters and discrete delay effects. Sufficient conditions are given to ensure the asymptotic stability of the semitrivial T-periodic solutions. A condition for permanence is also obtained by showing the existence of a positive global attractor enclosed by T-periodic functions. To substantiate our theoretical results, long-term behavior of the solutions for the time-delay system is numerically demonstrated.