Montréal, 4 - 7 décembre 2020
I will present a basic model for a single consumer and its resource in a two-season environment. I will give some basic properties of the model and explain how it differs from the purely continuous and the purely discrete analogues that have been studied for many decades. Then I will expand the model in two aspects: (i) I will consider coexistence mechanisms for many discrete-breeder consumers on a single limiting resource, and (ii) I will introduce spatial movement and present conditions for Turing pattern formation in such systems. This is joint work with Yunfeng Geng and Xiaoying Wang.
Then, we examine if and how the two different time lags and the switching time influence the existence and patterns of periodic solutions. We pay particular attention to the patterns involving multi-cycles within the prime period of the periodic solutions.