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

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...

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Main Authors:	Asmaa Idmbarek, Yamna Achik, Imane Agmour, Hajar Nafia, Youssef El Foutayeni
Format:	Article
Language:	English
Published:	Hindawi Limited 2021-01-01
Series:	Journal of Applied Mathematics
Online Access:	http://dx.doi.org/10.1155/2021/6619500

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spelling	doaj-65bbe4c6f2be4f27ae904b48014dc94a2021-03-08T02:01:42ZengHindawi LimitedJournal of Applied Mathematics1687-00422021-01-01202110.1155/2021/6619500Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility FunctionsAsmaa Idmbarek0Yamna Achik1Imane Agmour2Hajar Nafia3Youssef El Foutayeni4AnalysisAnalysisAnalysisAnalysisAnalysisIn 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.http://dx.doi.org/10.1155/2021/6619500
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Asmaa Idmbarek Yamna Achik Imane Agmour Hajar Nafia Youssef El Foutayeni
spellingShingle	Asmaa Idmbarek Yamna Achik Imane Agmour Hajar Nafia Youssef El Foutayeni Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions Journal of Applied Mathematics
author_facet	Asmaa Idmbarek Yamna Achik Imane Agmour Hajar Nafia Youssef El Foutayeni
author_sort	Asmaa Idmbarek
title	Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions
title_short	Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions
title_full	Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions
title_fullStr	Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions
title_full_unstemmed	Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions
title_sort	interrelationships between prey and predators and how predators choose their prey to maximize their utility functions
publisher	Hindawi Limited
series	Journal of Applied Mathematics
issn	1687-0042
publishDate	2021-01-01
description	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.
url	http://dx.doi.org/10.1155/2021/6619500
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Interrelationships between Prey and Predators and How Predators Choose Their Prey to Maximize Their Utility Functions

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