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Dynamics of predator–prey system with fading memory

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  • Sahoo, Banshidhar
  • Poria, Swarup

Abstract

A predator–prey model with fading memory for general Holling type functional response is proposed. The fading memory term is used with the hypothesis that the predator’s growth rate at present depends on the recent past quantities of prey. The effects of predator harvesting is also considered in the model. The model is analysed theoretically as well as numerically. Two parameter bifurcation analysis are done and the existence of Hopf point bifurcation is identified. Both supercritical and subcritical Hopf bifurcations are obtained with the variation of system parameters. Maximum sustainable yield with respect to harvesting effort is also determined. It is to be observed that the system dynamics is very rich in presence of fading memory. The obtained results may be useful in the field of agriculture and fishery.

Suggested Citation

  • Sahoo, Banshidhar & Poria, Swarup, 2019. "Dynamics of predator–prey system with fading memory," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 319-333.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:319-333
    DOI: 10.1016/j.amc.2018.11.013
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    References listed on IDEAS

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    1. Ghosh, Bapan & Kar, T.K., 2014. "Sustainable use of prey species in a prey–predator system: Jointly determined ecological thresholds and economic trade-offs," Ecological Modelling, Elsevier, vol. 272(C), pages 49-58.
    2. Pal, D. & Samanta, G.P. & Mahapatra, G.S., 2017. "Selective harvesting of two competing fish species in the presence of toxicity with time delay," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 74-93.
    3. Khajanchi, Subhas, 2017. "Modeling the dynamics of stage-structure predator-prey system with Monod–Haldane type response function," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 122-143.
    4. Liu, Chao & Lu, Na & Zhang, Qingling & Li, Jinna & Liu, Peiyong, 2016. "Modeling and analysis in a prey–predator system with commercial harvesting and double time delays," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 77-101.
    5. 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.
    6. Khajanchi, Subhas & Banerjee, Sandip, 2017. "Role of constant prey refuge on stage structure predator–prey model with ratio dependent functional response," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 193-198.
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    Cited by:

    1. Gökçe, Aytül, 2022. "A dynamic interplay between Allee effect and time delay in a mathematical model with weakening memory," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Yılmaz, Zeynep & Maden, Selahattin & Gökçe, Aytül, 2022. "Dynamics and stability of two predators–one prey mathematical model with fading memory in one predator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 526-539.

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