English

Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities

Dynamical Systems 2018-04-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1804.07641,
  title  = {Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities},
  author = {Martin Strugarek and Hongjun Ji},
  journal= {arXiv preprint arXiv:1804.07641},
  year   = {2018}
}
R2 v1 2026-06-23T01:29:58.375Z