课程名称：“The Dynamics of two phytoplankton species competing for light and nutrient with internal storage in a well-mixed water column”
授课地点：第二教学楼 2606 教室
Talk #1 “The Dynamics of two phytoplankton species competing for light and nutrient with internal storage in a well-mixed water column”
Abstract: In this talk we shall analyze a competition model of two phytoplankton species for a single nutrient with internal storage and light in a well-mixed aquatic environment. We apply the theory of monotone dynamical system to determine the competition outcomes , extinction of two species, competitive exclusion, stable coexistence, and bistability. We also present the graphical presentation to classify the competition outcomes.
Talk #2 “On the Mathematical Models of Intra-guild Predation
Abstract: The theory of Intra-guild predation was developed by Polis and Holt in 1990. Many works follow from their theory. However there are no experiments to justify their theory. In this talk we shall study the mathematical models with Droop type proposed by Huisman et based on their experiment in chemostat. First we consider ODE model and its mathematical analysis. We study the extinction and uniform persistence of the species. Then we consider the corresponding PDE models in unstirred chemostat. We establish the threshold dynamics for the growth of single species using the method developed in the paper of Hsu-Lam-Wang ( JMB 2017). Then we prove the uniform persistence of two species and conclude that intra-guild predation promotes the coexistence of the species. The talk is based on the joint works with Feng-Bin Wang and Nie Hua.
Talk #3 “Mathematical Models of Drug Resistance Bacteria”
Abstract: In this talk I first introduce my work with Paul Waltman on the simple chemostat with inhibition (SIAP 1992). In this work we consider a system of four equations for the dynamics of nutrient, wild-type, mutant and inhibitor. We reduced it to a system of three dimensional competitive system and apply Poicare-Bendixson Theorem. We present the results on extinction and existence of positive periodic solutions.
Next we propose a system of reaction diffusion equations with nutrient, wild-type and N mutants. The system is used to describe the dynamics of drug resistance bacteria in the paper of Kishony et. in Science 2016. We discuss two cases: forward mutation and forward-backward mutation. A Lyapunov functional is constructed to prove the global dynamics of the bacteria. This is a joint work with Jifa Jiang.
Talk#4 “A variable yield model of bacteria with wall growth in a chemostat”
Abstract: In this talk we shall discuss a variable yield model (Droop model) of the growth of bacteria with wall effect in a chemostat. We compare the results with the work of S. Pilyugin and P. Waltman in SIAP 1999. We also analyze the case in nano-chemostat ( Hsu&Yang in JMB(2016)) with Droop type.