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Stability and permanence of a discrete-time two-prey one-predator system with Holling Type-III functional response

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  • Banerjee, Ritwick
  • Das, Pritha
  • Mukherjee, Debasis

Abstract

This paper deals with the complex dynamical behavior of a discrete-time two-prey one-predator system with Holling Type-III functional response, coupled with inter-specific competition among the prey due to dietary overlap and intra-specific competition among the predators. The existence and local stability criteria of the steady states of the system are analyzed and the conditions for permanent co-existence of the three species are obtained. Finally, using a suitable example, some numerical simulations are performed to illustrate the rich dynamics of the system.

Suggested Citation

  • Banerjee, Ritwick & Das, Pritha & Mukherjee, Debasis, 2018. "Stability and permanence of a discrete-time two-prey one-predator system with Holling Type-III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 240-248.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:240-248
    DOI: 10.1016/j.chaos.2018.10.032
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    References listed on IDEAS

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    1. Elettreby, M.F., 2009. "Two-prey one-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2018-2027.
    2. Changjin Xu, 2012. "Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, September.
    3. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
    4. Cui, Qianqian & Zhang, Qiang & Qiu, Zhipeng & Hu, Zengyun, 2016. "Complex dynamics of a discrete-time predator-prey system with Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 158-171.
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    Cited by:

    1. Blé, Gamaliel & Dela-Rosa, Miguel Angel, 2019. "Neimark–Sacker bifurcation in a tritrophic model with defense in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 124-139.
    2. Li, Xinxin & Yu, Hengguo & Dai, Chuanjun & Ma, Zengling & Wang, Qi & Zhao, Min, 2021. "Bifurcation analysis of a new aquatic ecological model with aggregation effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 75-96.
    3. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Alsakaji, Hebatallah J. & Kundu, Soumen & Rihan, Fathalla A., 2021. "Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses," Applied Mathematics and Computation, Elsevier, vol. 397(C).

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