红楼Y论坛（第七十讲）-Spreading dynamics of an impulsive reaction-diffusion model with shifting environments

红楼Y论坛（第七十讲）

Topic: Spreading dynamics of an impulsive reaction-diffusion model with shifting environments

Time：10:00-11:00  June. 21, 2023(Wednesday）

Place：https://meeting.tencent.com/dm/BVsYidXBAQu8

578-672-022

Speaker：Yurong Zhang

Abstract： This paper focuses on the effects of environmental improvement and worsening on the spread and invasion of population with birth pulse. We propose an impulsive reaction-diffusion model with a shifting environment to describe the dynamics of species with distinct reproduction stage and dispersal stage.

First, the impulsive reaction-diffusion model is reduced to a discrete-time recursive system defined by a discrete map. Next, with the aid of the appropriate test function and comparison principle, we obtain some sufficient conditions on the nonexistence and uniqueness of nontrivial fixed points of the discrete map. This, combined with the abstract theory of spatially non-translation dynamical systems, enables us to establish the existence of traveling wave solutions and the asymptotic propagation properties of the model.