Basins of Attraction: Population Dynamics with Two Stable 4-cycles
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.
Henson, Shandelle M.; Costantino, R. F.; Desharnais, Robert A.; Cushing, J. M.; and Dennis, Brian, "Basins of Attraction: Population Dynamics with Two Stable 4-cycles" (2002). Faculty Publications. 2172.