Analysis of Dynamics in a Complex Food Chain with Ratio-Dependent Functional Response | Zendy

Michael Freeze | Zendy; Yaw Chang | Zendy; Wei Feng | Zendy

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Analysis of Dynamics in a Complex Food Chain with Ratio-Dependent Functional Response

Author(s) -

Michael Freeze,

Yaw Chang,

Wei Feng

Publication year - 2014

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2014002

Subject(s) - functional response , uniqueness , linearization , mathematics , extension (predicate logic) , multiplicity (mathematics) , biological system , statistical physics , control theory (sociology) , mathematical analysis , computer science , physics , predation , nonlinear system , ecology , control (management) , biology , quantum mechanics , artificial intelligence , programming language , predator

In this paper, we study a new model obtained as an extension of a three-species food chain model with ratio-dependent functional response. We provide non-persistence and permanence results and investigate the stability of all possible equilibria in relation to the ecological parameters. Results are obtained for the trivial and prey-only equilibria where the singularity of the model prevents linearization, and the remaining semi-trivial equilibria are studied using linearization. We provide a detailed analysis of conditions for existence, uniqueness, and multiplicity of coexistence equilibria, as well as permanent eect for all species. The complexity of the dynamics in this model is theoretically discussed and graphically demonstrated through various examples and numerical simulations.

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