Multiple attractors and resonance in periodically forced population models

Oscillating discrete autonomous dynamical systems admit multiple oscillator y solutions in the advent of periodic forcing. The multiple cycles are out of phase, and some of their averages may resonate with the forcing amplitud e while others attenuate. Tn application to population biology, populations with stable inherent oscillations in constant habitats are predicted to de velop multiple attracting oscillatory final states in the presence of habit at periodicity. The average total population size may resonate or attenuate with the amplitude of the environmental fluctuation depending on the initi al population size. The theory has been tested successfully in the laborato ry by subjecting cultures of the flour beetle Tribolium to habitat periodic ity of various amplitudes. (C) 2000 Elsevier Science B.V. All rights reserv ed.