Uniqueness and stability of time-periodic pyramidal fronts for a periodic competition-diffusion system

Abstract

The existence, non-existence and qualitative properties of time periodic pyramidal traveling front solutions for the time periodic Lotka-Volterra competition-diffusion system have already been studied in $ \Bbb{R}^{N} $ with $ N\geq 3 $. In this paper, we continue to study the uniqueness and asymptotic stability of such time-periodic pyramidal traveling front in the three-dimensional whole space. For any given admissible pyramid, we show that the time periodic pyramidal traveling front is uniquely determined and it is asymptotically stable under the condition that given perturbations decay at infinity. Moreover, the time periodic pyramidal traveling front is uniquely determined as a combination of two-dimensional periodic V-form waves on the edges of the pyramid.