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An optimal control problem for a predator–prey model with strong and weak preys

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  • Rebelo, Paulo
  • Rosa, Silvério

Abstract

The aim of this paper is to study an optimal control problem for a non-autonomous model with one predator and two prey species, one strong and the other weak. The resulting model incorporates a weak Allee effect in the strong prey, seasonal breeding in both preys, and an extra-food supply. The model takes into account the death rate of predators, which results in a decrease in their biomass. We prove the existence, uniqueness, and qualitative properties of the solutions. The optimal control problem aims to control the predator population by considering three strategies. Simulation results show the usefulness and efficacy of the proposed control measures to manage the predator biomass.

Suggested Citation

  • Rebelo, Paulo & Rosa, Silvério, 2025. "An optimal control problem for a predator–prey model with strong and weak preys," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013900
    DOI: 10.1016/j.chaos.2024.115838
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    References listed on IDEAS

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    1. Yong Ye & Hua Liu & Yu-mei Wei & Ming Ma & Kai Zhang, 2019. "Dynamic Study of a Predator‐Prey Model with Weak Allee Effect and Delay," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    2. Jana, Soovoojeet & Ghorai, Abhijit & Guria, Srabani & Kar, T.K., 2015. "Global dynamics of a predator, weaker prey and stronger prey system," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 235-248.
    3. Rosa, S. & Rebelo, P. & Silva, C.M. & Alves, H. & Carvalho, P.G., 2018. "Optimal control of the customer dynamics based on marketing policy," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 42-55.
    4. Pati, N.C. & Layek, G.C. & Pal, Nikhil, 2020. "Bifurcations and organized structures in a predator-prey model with hunting cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Hui-Chih Hung & Yu-Chih Chiu & Muh-Cherng Wu, 2017. "A Modified Lotka–Volterra Model for Diffusion and Substitution of Multigeneration DRAM Processing Technologies," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-12, May.
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