Spatiotemporal dynamics in a diffusive predator–prey model with group defense and nonlocal competition

Abstract

A nonlocal prey competition term, which represents a spatially weighted average of prey density, is incorporated into a diffusive predator–prey model with group defense effect to investigate the corresponding dynamic behaviors. By analyzing the distribution of eigenvalues and using the gestation time delay of predators as a bifurcation parameter, we discuss the stability of positive equilibrium and the existence of Hopf bifurcation. Based on the extended center manifold method and normal form theory, the direction and stability of the bifurcating periodic solution are discussed. Finally, spatially inhomogeneous oscillations are observed near the Hopf bifurcation.