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Existence of limit cycles in a tritrophic food chain model with Holling functional responses of type II and III
Author(s) -
Blé Gamaliel,
Castellanos Víctor,
Llibre Jaume
Publication year - 2016
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.3842
Subject(s) - functional response , mathematics , limit (mathematics) , trophic level , food chain , type (biology) , limit cycle , predator , predation , stability (learning theory) , control theory (sociology) , mathematical analysis , ecology , biology , computer science , control (management) , machine learning , artificial intelligence
We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species, Holling III and Holling II functional response for the predator and the top‐predator, respectively. We prove that this model has stable periodic orbits for adequate values of its parameters. Copyright © 2016 John Wiley & Sons, Ltd.