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

Asmaa Idmbarek | Zendy; Yamna Achik | Zendy; Imane Agmour | Zendy; Hajar Nafia | Zendy; Youssef El Foutayeni | Zendy

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

Author(s) -

Asmaa Idmbarek,

Yamna Achik,

Imane Agmour,

Hajar Nafia,

Youssef El Foutayeni

Publication year - 2021

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2021/6619500

Subject(s) - predation , complementarity (molecular biology) , profit (economics) , mathematical optimization , predator , nash equilibrium , mathematics , mathematical economics , ecology , economics , microeconomics , biology , genetics

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.

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