Multiple attractors, saddles, and population dynamics in periodic habitats

Mathematical models predict that a population which oscillates in the absen ce of time-dependent factors can develop multiple attracting final states i n the advent of periodic forcing. A periodically-forced, stage-structured m athematical model predicted the transient and asymptotic behaviors of Tribo lium (flour beetle) populations cultured in periodic habitats of fluctuatin g flour volume. Predictions included multiple (2-cycle) attractors, resonan ce and attenuation phenomena, and saddle influences. Stochasticity, combine d with the deterministic effects of an unstable 'saddle cycle' separating t he two stable cycles, is used to explain the observed transients and final states of the experimental cultures. In experimental regimes containing mul tiple attractors, the presence of unstable invariant sets, as well as stoch asticity and the nature, location, and size of basins of attraction, are al l central to the interpretation of data. (C) 1999 Society for Mathematical Biology.