Numerical existence and stability of solutions to the distributed spruce budworm model

Abstract

This paper presents the steady-state solutions and traveling wave solutions for a spatially distributed PDE version of the spruce budworm model. The ODE (undistributed) model has been used in practical scenarios to model the outbreaks of the spruce budworm in forest environments, alongside the study of concepts involving fixed points and bifurcations in introductory differential equations courses. This study represents the spread of an outbreak from one end of a forest to the other. Numerical simulations are conducted using spectral methods.