Neimark–Sacker bifurcation in a tritrophic model with defense in the prey

Gamaliel Blé and Miguel Angel Dela-Rosa

Chaos, Solitons & Fractals, 2019, vol. 123, issue C, 124-139

Abstract: We analyze a tritrophic discrete system. The analysis focuses in two cases, the two dimensional one in which the absence of super-predator lead to a predator-prey discrete system; secondly, we consider a model constructed using the average grow method in each density of the species. In both cases, we prove that the coexistence of species takes place by means of a supercritical Neimark–Sacker bifurcation at one of the fixed points that the system could have. We assume that the lowest trophic level has logistic grow and the functional responses for predators-prey and superpredator-mesopredator are Holling type IV.

Keywords: Neimark–Sacker bifurcation; Discrete–Time tritrophic model; Holling functional responses (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:123:y:2019:i:c:p:124-139

DOI: 10.1016/j.chaos.2019.03.034

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