Predator-prey models in periodically fluctuating environments

A class of ordinary or integrodifferential equations describing predator-prey dynamics is considered under the assumption that the coefficients are periodic functions of time. This class is characterized by the logistic behaviour of the prey in the absence of predators and it includes the Leslie model. We show that there exists a periodic solution provided that the average of the predator's intrinsic rate of increase is greater than a critical value. We use well-known results in bifurcation theory for nonlinear eigenvalue problems, as well as an extension to the case of non-globally defined operators of some recent results on the global nature of branches of solutions.

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