March 6, 2020
Summary
Xiaoyuan Chang (Harbin University of Science and Technology) Analysis of a stoichiometric bacteria-grazer reaction-diffusion model for organic matter biodegradation - AND - Junping Shi (William & Mary): Modeling animal movement with memory with partial differential equations with time-delay
Full Description
Xiaoyuan Chang Abstract: The dynamical behaviors of a bacteria-carbon-nitrogen reaction-diffusion system with grazers and without grazers are investigated in this paper. It is shown that the bacteria death rate and the grazer death rate play a decisive role in the dynamics of the system. The existence, stability and persistence of the solutions are proved by applying the theorem of existence of eigenvalue, the local and global bifurcation theory, and the abstract persistence theory. Through numerical simulations, the transient dynamic and the oscillation phenomenon are obtained.
Junping Shi Abstract: Animal populations often self-organize into territorial structure from movements and interactions of individual animals. Memory is one of cognitive processes that may affect the movement and navigation of the animals. We will review several mathematical approaches of animal spatial movements, and also introduce our recent work using partial differential equations with time-delay to model and simulate the memory-based movement. We will show the bifurcation and pattern formation for such models. It is based on joint work with Chuncheng Wang, Hao Wang, Xiangping Yan, Qingyan Shi and Yongli Song.
