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

  •  Enobong E. Joshua    
  •  Ekemini T. Akpa    


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.

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