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Memory effect on Bazykin’s prey-predator model: Stability and bifurcation analysis

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  • Ghosh, Uttam
  • Pal, Swadesh
  • Banerjee, Malay

Abstract

This paper deals with a system of two fractional order differential equations for prey-predator interaction with intra-specific competition among predators. The fractional order differential equation is considered in the sense of Caputo derivative and the derivation of the fractional order model is explained in terms of memory effect on population growth. Detailed mathematical results are provided to establish the positiveness, existence–uniqueness and boundedness of the solutions. The conditions required for local asymptotic stability of various equilibrium points and global stability of coexistence equilibrium are derived along with the Hopf-bifurcation condition for coexistence equilibrium. The effect of memory on the system dynamics through the shift of Hopf-bifurcation threshold is demonstrated with the help of exhaustive numerical simulations. This study also reveals the effect of memory based growth on global bifurcation threshold.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309231
    DOI: 10.1016/j.chaos.2020.110531
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    Cited by:

    1. Balcı, Ercan, 2023. "Predation fear and its carry-over effect in a fractional order prey–predator model with prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Shang, Zuchong & Qiao, Yuanhua & Duan, Lijuan & Miao, Jun, 2021. "Bifurcation analysis and global dynamics in a predator–prey system of Leslie type with an increasing functional response," Ecological Modelling, Elsevier, vol. 455(C).
    3. 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.
    4. Avcı, İbrahim & Hussain, Azhar & Kanwal, Tanzeela, 2023. "Investigating the impact of memory effects on computer virus population dynamics: A fractal–fractional approach with numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Majumdar, Prahlad & Mondal, Bapin & Debnath, Surajit & Ghosh, Uttam, 2022. "Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. 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).

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