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Rich dynamics of a discrete two dimensional predator–prey model using the NSFD scheme

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  • Mokni, Karima
  • Ch-Chaoui, Mohamed
  • Mondal, Bapin
  • Ghosh, Uttam

Abstract

In this paper, we consider a two-species predator–prey model with Holling type III functional response and non-linear predator harvesting. The proposed model is discretized using a non-standard finite difference scheme (NSFD). The stability of different equilibrium points are analyzed. Also, the conditions of various types of bifurcations likely: Transcritical, Neimark–Sacker bifurcation (NSB), and Flip (Period doubling) bifurcation (PDB) have been established along with chaos control strategies. The numerical results indicate that the system exhibits different patterns of solutions, including single, two, and higher periodicity. Using Lyapunov exponents and bifurcation diagrams, chaotic solutions are verified. Two model parameters were drawn simultaneously in the attractor basin, which yielded different periodic solutions compared to the continuous dynamical system. Lastly, the pole placement method (PPM) has been used to control chaos in the proposed discrete ecological model.

Suggested Citation

  • Mokni, Karima & Ch-Chaoui, Mohamed & Mondal, Bapin & Ghosh, Uttam, 2024. "Rich dynamics of a discrete two dimensional predator–prey model using the NSFD scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 992-1018.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:992-1018
    DOI: 10.1016/j.matcom.2023.09.024
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    References listed on IDEAS

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    1. Terefe, Y.A. & Njagarah, J.B.H. & Kassa, S.M., 2023. "Effect of cross-border migration on the healthcare system of a destination community: Insights from mathematical modelling of COVID-19 in a developing country," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 444-479.
    2. Chou, Yen-hsi & Chow, Yunshyong & Hu, Xiaochuan & Jang, Sophia R.-J., 2021. "A Ricker–type predator–prey system with hunting cooperation in discrete time," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 570-586.
    3. Mondal, Bapin & Ghosh, Uttam & Rahman, Md Sadikur & Saha, Pritam & Sarkar, Susmita, 2022. "Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 111-135.
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