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Local stability analysis of ratio-dependent predator–prey models with predator harvesting rates

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  • Heggerud, Christopher M.
  • Lan, Kunquan

Abstract

We study the local stability of ratio-dependent predator–prey models with nonconstant predator harvesting rates. We provide more general conditions on the parameters involved in the models under which the models are locally stable or unstable at the two positive equilibria. We show that the predator free positive equilibrium can be a stable node or saddle-node and the positive interior equilibrium can be a stable or unstable node or focus or a center point depending on the ranges of the parameters involved. Our results generalize and improve some known results and show that the models have more rich dynamics than those ratio-dependent predator–prey models without any harvesting rates.

Suggested Citation

  • Heggerud, Christopher M. & Lan, Kunquan, 2015. "Local stability analysis of ratio-dependent predator–prey models with predator harvesting rates," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 349-357.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:349-357
    DOI: 10.1016/j.amc.2015.08.062
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    Cited by:

    1. Sahoo, Banshidhar & Poria, Swarup, 2019. "Dynamics of predator–prey system with fading memory," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 319-333.
    2. Sk Golam Mortoja & Prabir Panja & Shyamal Kumar Mondal, 2023. "Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    3. Mansal, Fulgence & Sene, Ndolane, 2020. "Analysis of fractional fishery model with reserve area in the context of time-fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Zhang, Yan & Chen, Shihua & Gao, Shujing & Wei, Xiang, 2017. "Stochastic periodic solution for a perturbed non-autonomous predator–prey model with generalized nonlinear harvesting and impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 347-366.

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