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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.
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)
Full Text: DOI
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