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Coexistence of species in a tritrophic food chain model with Holling functional response type IV
Author(s) -
Blé Gamaliel,
Castellanos Víctor,
DelaRosa Miguel A.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5184
Subject(s) - functional response , mathematics , hopf bifurcation , supercritical fluid , predation , food chain , trophic level , type (biology) , bifurcation , equilibrium point , differential equation , mathematical analysis , nonlinear system , ecology , thermodynamics , biology , predator , physics , quantum mechanics
We determine conditions on the parameters of a tritrophic food chain model, implying the coexistence of the species. We consider that both predators corresponding to middle and top trophic levels have Holling functional responses type IV, and the prey at the lower trophic level has either linear or logistic growth rate. We prove that the differential system has an equilibrium point in which it exhibits a supercritical Hopf bifurcation independently of the growth rate of the prey. In the logistic case, we prove the existence of at least three equilibrium points in the positive octant and one of them exhibits a supercritical Hopf bifurcation.