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Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions

Author

Listed:
  • Asmaa Idmbarek
  • Yamna Achik
  • Imane Agmour
  • Hajar Nafia
  • Youssef El Foutayeni

Abstract

In this work, we model the relationship between prey and predators by studying the interactive behavior of this prey‐predator model and using the change of prey. The objective is to maximize the profit function of each predator by seeking the strategy provided by each predator to maximize its profit. To do so, we maximize this utility function being constrained by balance equations between biomass and trophic, and we show that this last problem is completely equivalent to finding the generalized Nash equilibrium point. To calculate it, we use the conditions of Karush‐Kuhn‐Tucker and we show that it is indeed a linear complementarity problem.

Suggested Citation

  • Asmaa Idmbarek & Yamna Achik & Imane Agmour & Hajar Nafia & Youssef El Foutayeni, 2021. "Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnljam:v:2021:y:2021:i:1:n:6619500
    DOI: 10.1155/2021/6619500
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    References listed on IDEAS

    as
    1. Yamna Achik & Asmaa Idmbarek & Hajar Nafia & Imane Agmour & Youssef El foutayeni, 2020. "A Fast Algorithm for Solving a Class of the Linear Complementarity Problem in a Finite Number of Steps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    2. Yamna Achik & Asmaa Idmbarek & Hajar Nafia & Imane Agmour & Youssef El foutayeni, 2020. "A Fast Algorithm for Solving a Class of the Linear Complementarity Problem in a Finite Number of Steps," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-8, December.
    3. T. Suebcharoen, 2017. "Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-11, September.
    4. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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