Asymptotic periodicity and permanence in a competition-diffusion system with discrete delays
Applied Mathematics and Computation - Special issue on differential equations and computational simulations II
Convergence of solutions of reaction-diffusion systems with time delays
Nonlinear Analysis: Theory, Methods & Applications
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This paper is concerned with a time-delayed Lotka-Volterra competition reaction-diffusion system with homogeneous Neumann boundary conditions. Some explicit and easily verifiable conditions are obtained for the global asymptotic stability of all forms of nonnegative semitrivial constant steady-state solutions. These conditions involve only the competing rate constants and are independent of the diffusion-convection and time delays. The result of global asymptotic stability implies the nonexistence of positive steady-state solutions, and gives some extinction results of the competing species in the ecological sense. The instability of the trivial steady-state solution is also shown.