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

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 bound-edness 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 va-lidity of theoretical findings.