The effects of seasonality on discrete models of population growth.

*(English)*Zbl 0551.92014The effects of seasonality on the dynamics of a bivoltine population with discrete, nonoverlapping generations are examined. It is found that large seasonality is inevitably destabilizing but that mild seasonality may have a pronounced stabilizing effect. Seasonality also allows for the coexistence of alternative stable states (equilibria, cycles, chaos).

These solutions may be seasonally in-phase, out-of-phase, or asynchronous. In-phase solutions correspond to winter regulation of population density, whereas out-of-phase solutions correspond to summer regulation. Analysis suggests that summer regulation is possible only in mildly seasonal habitats.

These solutions may be seasonally in-phase, out-of-phase, or asynchronous. In-phase solutions correspond to winter regulation of population density, whereas out-of-phase solutions correspond to summer regulation. Analysis suggests that summer regulation is possible only in mildly seasonal habitats.

##### Keywords:

effects of seasonality; dynamics of a bivoltine population; discrete, nonoverlapping generations; coexistence of alternative stable states; equilibria, cycles, chaos; In-phase solutions; out-of-phase solutions
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\textit{M. Kot} and \textit{W. M. Schaffer}, Theor. Popul. Biol. 26, 340--360 (1984; Zbl 0551.92014)

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