UAlberta Math Biology Seminar: Juping Ji

In this talk, I will introduce two ecological models with intraguild predation. I will first focus on developing a novel mathematical model that couples a competition model with an intraguild predation model via dispersal of intraguild prey driven by intraguild predator-avoidance. I will show that a large dispersal rate would lead to the collapse of species coexistence, while three modes of species coexistence are possible when the intraguild prey dispersal rate is not too large. Then, an intraguild predation model with intraguild predator diffusion will be proposed and studied. For the resulting partially degenerate reaction-diffusion system, I will show that the solution semiflow is bounded dissipative and the positive orbits of bounded sets are bounded. Moreover, I will show that intraguild predator diffusion can lead to the occurrence of spatially nonhomogeneous oscillations and spatiotemporal chaos and can induce transitions between spatially homogeneous oscillations, spatially nonhomogeneous oscillations and chaos.