# Bifurcation in a Model of Spruce Budworm Populations

Bifurcation in a Model of Spruce Budworm Populations

Spruce budworm populations have in recent decades become a classic case study in mathematical biology. This Demonstration illustrates the bifurcation that occurs as a certain parameter is varied in a two-component model of budworm and foliage densities. The parameter is directly related to the size of a predatory population of birds. The plot on the left shows the graphs of these densities versus time, and the plot on the right shows the corresponding phase-plane orbit, nullclines, and equilibrium points.