Spatiotemporal patterns of a structured spruce budworm diffusive model

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. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

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 exhibits bistability due to nonlinear birth function and predation by birds. We establish results on the stability and global Hopf bifurcation from the spatially homogeneous steady state with maturation delay as a bifurcation parameter. We also use degree theory to determine the diffusion rate intervals for spatially heterogeneous steady states. Numerical experiments demonstrate interesting spatial-temporal patterns.