Spatial Dynamics of a Diffusive Prey-Predator Model with Stage Structure and Fear Effect (Journal of Nonlinear Modeling and Analysis, 2024)
To understand the influence of fear effect on population dynamics,especially for the populations with obvious stage structure characteristics, wepropose and investigate a diffusive prey-predator model with stage structurein predators. First, we discuss the existence and stability of equilibrium ofthe model in the absence of diffusion. Then, we obtain the critical conditionsfor Hopf and Turing bifurcations. Some numerical simulations are also carriedout to verify our theoretical results, which indicate that the fear can inducethe prey population to show five pattern structures: cold-spot pattern, mixedpattern with cold spots and stripes, stripes pattern, hot-spot pattern, mixedpattern with hot spots and stripes. These findings imply that the fear effect induced by the mature predators plays an important role in the spatialdistribution of species.
Keywords: Prey-predator model; Fear effect; Stage-structured model; Hopf bifurcation; Turing bifurcation; Pattern formation.