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Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities. (English) Zbl 1398.37093
Summary: We consider a biological population whose environment varies periodically in time, exhibiting two very different “seasons”: one is favorable and the other one is unfavorable. For monotone differential models with concave nonlinearities, we address the following question: the system’s period being fixed, under what conditions does there exist a critical duration for the unfavorable season? By “critical duration” we mean that above some threshold, the population cannot sustain and extincts, while below this threshold, the system converges to a unique periodic and positive solution. We term this a “sharp seasonal threshold property” (SSTP, for short).
Building upon a previous result, we obtain sufficient conditions for SSTP in any dimension and apply our criterion to a two-dimensional model featuring juvenile and adult populations of insects.
##### MSC:
 37N25 Dynamical systems in biology 34D23 Global stability of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 92D25 Population dynamics (general)
##### Keywords:
periodic forcing; seasonality; population dynamics
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##### References:
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