Multiple attractors in a discrete competition model

Abstract

The existence of multiple attractors in a competition model implies that the question of coexistence vs. extinction can depend on initial conditions. A discrete stage-structured model of two competing species is derived from a well-tested single-species model of insect populations, and is shown to exhibit multiple attractors for parameter values similar to those used in laboratory experiments which demonstrated chaos in population dynamics. The corresponding basins of attraction are investigated and shown to have very complex structures, and the initial stage structure of the populations is shown to have a significant impact on final outcomes.