Dynamics of Ecological Models with Intraguild Predation
University of New Brunswick
This dissertation consists of five chapters. A literature review on intraguild predation models is given in Chapter 1. For the convenience of presentation, some basic concepts and results on dynamical systems are introduced in Chapter 1 as well. In Chapter 2, an intraguild predation model with a Beddington–DeAngelis functional response is investigated. The focus is on the existence, local and global stability of all feasible equilibria and uniform persistence of the model. Numerical simulations are performed to explore the influence of intraguild predator interference and intraguild predation on model dynamics. In Chapter 3, I develop 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 show that large dispersal rate would lead to the collapse of species coexistence. In addition, I show that three modes of species coexistence are possible when the intraguild prey dispersal rate is not too large. An intraguild predation model with intraguild predator diffusion is proposed and studied in Chapter 4. It is shown that the local system can have four boundary equilibria and at most two interior equilibria. In my three-species intraguild predation model, only intraguild predator diffusion is considered. This results in a partially degenerate reaction-diffusion system. For this partially degenerate system, I show that the solution semiflow is bounded dissipative and the positive orbits of bounded sets are bounded. I also demonstrate that intraguild predator diffusion can lead to the occurrence of spatially nonhomogeneous oscillations and spatiotemporal chaos. Further, I show that intraguild predator diffusion can induce transitions between spatially homogeneous oscillations, spatially nonhomogeneous oscillations and chaos. Chapter 5 summarizes the main results of this dissertation and suggests some possible future work on intraguild predation models.