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

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  • Enobong E. Joshua
  • Ekemini T. Akpa

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.

Suggested Citation

  • Enobong E. Joshua & Ekemini T. Akpa, 2018. "Spirals and Cycles of Biological Systems via Extended Rosenzweig-MacArthur Model with Ratio-dependent Functional Response," Modern Applied Science, Canadian Center of Science and Education, vol. 12(9), pages 149-149, September.
    • Handle: RePEc:ibn:masjnl:v:12:y:2018:i:9:p:149
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    1. Enobong E. Joshua & Ekemini T. Akpan, 2018. "Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model," Modern Applied Science, Canadian Center of Science and Education, vol. 12(2), pages 171-171, February.
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      JEL classification:

      • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
      • Z0 - Other Special Topics - - General

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