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

Michael Freeze; Yaw Chang; Wei Feng

doi:10.11948/2014002

2014 Volume 4 Issue 1

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Michael Freeze, Yaw Chang, Wei Feng. Analysis of Dynamics in a Complex Food Chain with Ratio-Dependent Functional Response[J]. Journal of Applied Analysis & Computation, 2014, 4(1): 69-87. doi: 10.11948/2014002

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Michael Freeze, Yaw Chang, Wei Feng. Analysis of Dynamics in a Complex Food Chain with Ratio-Dependent Functional Response[J]. Journal of Applied Analysis & Computation, 2014, 4(1): 69-87. doi: 10.11948/2014002

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

Mathematics and Statistics Department, University of North Carolina Wilmington, Wilmington, NC 28403-5970, USA

Abstract

Abstract

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 effect for all species. The complexity of the dynamics in this model is theoretically discussed and graphically demonstrated through various examples and numerical simulations.
- Coexistence and Permanence /
- local and global stability /
- asymptotic behavior /
- population dynamics /
- ratio-dependent food chain /
- numerical simulations
MSC: 34A34;34C11;34D20

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