Spatiotemporal dynamics induced by intraguild predator diffusion in an intraguild predation model

An intraguild predation model with intraguild predator diffusion is proposed and studied in this work. It is shown that the local system can have four boundary equilibria and at most two interior equilibria. The interior equilibria may exist even when the system is not uniformly persistent. When only intraguild predator diffusion is incorporated into our three-species model, the resulting model is a partially degenerate reaction-diffusion system. For this partially degenerate system, we show that the solution semiflow is bounded dissipative and the positive orbits of bounded sets are bounded. We also demonstrate that intraguild predator diffusion can lead to the occurrence of spatially nonhomogeneous oscillations and spatiotemporal chaos. Further, we show that intraguild predator diffusion can induce transitions between spatially homogeneous oscillations, spatially nonhomogeneous oscillations and chaos.