Basins of attraction: population dynamics with two stable 4‐cycles

Abstract

We use the concepts of composite maps, basins of attraction, basin switching, and saddle fly‐by's to make the ecological hypothesis of the existence of multiple attractors more accessible to experimental scrutiny. Specifically, in a periodically forced insect population growth model we identify multiple attractors, namely, two locally stable 4‐cycles. Using the model‐predicted basins of attraction, we examine data time series from a Tribolium experiment for evidence of the multiple attractors. We conclude that the multiple attractor hypothesis together with demographic stochasticity accounts for the experimental observations.