| Volume 4, Number 1, 2014, Pages 69-87 DOI：10.11948/2014002 |
| Analysis of Dynamics in a Complex Food Chain with Ratio-Dependent Functional Response |
| Michael Freeze,Yaw Chang,Wei Feng |
| Keywords:Coexistence and Permanence |
| Abstract: |
| In this paper, we study a new model obtained as an extension of athree-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 tothe ecological parameters. Results are obtained for the trivial andprey-only equilibria where the singularity of the model prevents linearization, and the remaining semi-trivial equilibria are studiedusing linearization. We provide a detailed analysis of conditionsfor existence, uniqueness, and multiplicity of coexistencee quilibria, as well as permanent effect for all species. The complexity of the dynamics in this model is theoretically discussedand graphically demonstrated through various examples and numerical simulations. |
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