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Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses

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  • Alsakaji, Hebatallah J.
  • Kundu, Soumen
  • Rihan, Fathalla A.

Abstract

In this paper, we study the dynamics of a delay differential model of predator-prey system involving teams of two-prey and one-predator, with Monod-Haldane and Holling type II functional responses, and a cooperation between the two-teams of preys against predation. We assume that the preys grow logistically and the rate of change of the predator relies on the growth, death and intra-species competition for the predators. Two discrete time-delays are incorporated to justify the reaction time of predator with each prey. The permanence of such system is proved. Local and global stabilities of interior steady states are discussed. Hopf bifurcation analysis in terms of time-delay parameters is investigated, and threshold parameters τ1* and τ2* are obtained. Sensitivity analysis that measures the impact of small changes in the model parameters into the model predictions is also investigated. Some numerical simulations are provided to show the effectiveness of the theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308729
    DOI: 10.1016/j.amc.2020.125919
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Singh, Brahampal, 2007. "The dynamics of a food web consisting of two preys and a harvesting predator," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1346-1356.
    2. 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).
    3. F. A. Rihan & H. J. Alsakaji & C. Rajivganthi, 2020. "Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect," Complexity, Hindawi, vol. 2020, pages 1-15, January.
    4. 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.
    5. Elettreby, M.F., 2009. "Two-prey one-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2018-2027.
    6. Wang, Weiming & Wang, Hailing & Li, Zhenqing, 2007. "The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1772-1785.
    7. Mbava, W. & Mugisha, J.Y.T. & Gonsalves, J.W., 2017. "Prey, predator and super-predator model with disease in the super-predator," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 92-114.
    8. Zeng, Ting & Teng, Zhidong & Li, Zhiming & Hu, Junna, 2018. "Stability in the mean of a stochastic three species food chain model with general Le´vy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 258-265.
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