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Multiple attractors and resonance in periodically forced population models. (English) Zbl 0957.37018
Discrete autonomous dynamical systems with periodic solutions admit multiple oscillatory solutions in the advent of periodic forcing. In general, the multiple cycles are mutually out of phase, and some of the cycle averages may increase with the forcing amplitude while others decrease. The multiple cycles differ in phase, and may differ in average total population size as well. The author shows that the average total population size may resonate or attenuate with the amplitude of the environmental fluctuation depending on the initial population size. The author applies his result to the periodic LPA model, Tribolium populations were maintained in periodically forced flour habitats of constant $$20g$$, alternating $$2s-12g$$, and alternating $$32-12g$$.

##### MSC:
 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics 37N25 Dynamical systems in biology
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