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Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model

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  • Enobong E. Joshua
  • Ekemini T. Akpan

Abstract

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptotically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values.Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:masjnl:v:12:y:2018:i:2:p:171
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    References listed on IDEAS

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    1. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar, 2014. "Top-predator interference and gestation delay as determinants of the dynamics of a realistic model food chain," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 50-63.
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    Cited by:

    1. 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.

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    More about this item

    JEL classification:

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

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