Ecological outbreak dynamics and the cusp catastrophe

Many ecological processes exhibit trajectories which can be suitably represented by stable equilibria or smooth limit cycles. However, a third kind of ecological process involves intermittent, abrupt, and drastic changes in densities, here termed outbreak dynamics, which require different modelling frameworks. One such framework, the cusp catastrophe, is used here in a modelling study of a particular outbreak insect, the forest tent caterpillar. This model is then generalized to cover a set of related ecological systems. The particular form of the model for each system depends on whether the major controlling ecological variables are externally imposed, or are incorporated in the model equations. It is concluded that the simple cusp catastrophe is an appropriate metaphor for understanding outbreak dynamics.