Spatiotemporal patterns of a structured spruce budworm diffusive model

Abstract

We formulate and analyze a general reaction-diffusion equation with delay, inspired by age-structured spruce budworm population dynamics with spatial diffusion by matured individuals. The model has its particular feature for bistability due to the incorporation of a nonlinear birth function (Ricker's function) and a Holling type function of predation by birds. Here we establish some results about the global dynamics, in particular, the stability of and global Hopf bifurcation from the spatially homogeneous steady state when the maturation delay is taken as a bifurcation parameter. We also use a degree theoretical argument to identify intervals for the diffusion rate when the model system has a spatially heterogeneous steady state. Numerical experiments presented show interesting spatialtemporal patterns.