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Dynamics and stability of two predators–one prey mathematical model with fading memory in one predator

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  • Yılmaz, Zeynep
  • Maden, Selahattin
  • Gökçe, Aytül

Abstract

This paper concentrates on dynamics and stability analysis of two predators–one prey mathematical model with competition between predators and fading memory in one predator. The investigation of the constructed model shows that there exist five equilibria, e.g. trivial extinction state of all populations, extinction of both predators state, extinction of first or second predator state and coexisting state. Investigating the eigenvalues of characteristic polynomial, conditions for the local stability around each equilibrium are also determined depending on the parameter space. Analytical formulations are complemented with numerical simulations, where time simulations and single parameter numerical continuation of each variable are performed with respect to model parameters and multiple sub-and super-critical Hopf bifurcations, period doubling bifurcation and transcritical bifurcation are detected for different values of memory related parameter. Our results show that fading memory and competition between predators have substantial impact on the existence and dynamics of all three populations and may shed lights on further understanding of interacting species in ecology.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:202:y:2022:i:c:p:526-539
    DOI: 10.1016/j.matcom.2022.07.023
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    References listed on IDEAS

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    1. Peter Chesson & Jessica J. Kuang, 2008. "The interaction between predation and competition," Nature, Nature, vol. 456(7219), pages 235-238, November.
    2. 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.
    3. Sahoo, Banshidhar & Poria, Swarup, 2019. "Dynamics of predator–prey system with fading memory," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 319-333.
    4. Ghosh, Uttam & Pal, Swadesh & Banerjee, Malay, 2021. "Memory effect on Bazykin’s prey-predator model: Stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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