Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities

Martin Strugarek (1, 2, 3) , Hongjun Ji (3)

1 AgroParisTech
2 MAMBA - Modelling and Analysis for Medical and Biological Applications
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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.

Mots clés: Seasonality; Dynamical systems; Population dynamics; Periodic forcing

Domaines: Systèmes dynamiques [math.DS]

Martin Strugarek, Hongjun Ji. Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities. 2018. ⟨hal-01772628⟩