Propagation dynamics for nonlinear evolution systems in a shifting environment

Abstract

Spatial and temporal heterogeneities play a crucial role in population biology. In particular, climate change and intensi ed environmental pressures have highlighted the signi cance of shifting habitats as a framework for understanding their impact on population dynamics. As a result, this thesis is devoted to the investigation of spreading properties and traveling waves for three classes of evolution systems in shifting habitats. An overview of the mathematical analysis of propagation phenomena and shifting habitat problems is presented in the introduction. The main theoretical tools used in this thesis are presented in the preliminaries. In Chapter 3, we rst consider a species living in an environment surrounded by two favorable habitats. To describe its dynamics, we study a nonmonotone integro-di erence equation with a nonsymmetric dispersal kernel. In Chapter 4, to understand the e ects of climate change and industrialization on a population with juvenile and adult stages, we propose a stage-structured model and explore its propagation dynamics in a habitat that shifts from unfavorable to favorable habitats. In Chapter 5, for species whose juveniles have more limited dispersal ability than adults, we further investigate a time-delayed reaction-di usion equation in a time-periodic shifting environment surrounded by two unfavorable habitats. At the end of this thesis, we present some open problems and directions for future research.