Spirals and Cycles of Biological Systems via Extended Rosenzweig-MacArthur Model with Ratio-dependent Functional Response

Enobong E. Joshua and Ekemini T. Akpa

Modern Applied Science, 2018, vol. 12, issue 9, 149

Abstract: This paper investigates stable proper nodes, stable spiral sinks and  stable  ω−limit cycles of Extended Rosenzweig-MacAthur Model, which incorporates ratio-dependent functional response on predation mechanism. The ultimate boundedness condition has been used to predict extinction, co-existence, and exponential convergence scenarios of the model. The Poincare-Bendixson results guarantee existence of periodic cycles of the models. The system degenerate from stable spiral sinks to stable  ω−limit cycles as control parameter varies. Numerical simulations are provided to support the validity of theoretical findings.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:masjnl:v:12:y:2018:i:9:p:149

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