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

Asmaa Idmbarek,Yamna Achik,Hajar Nafia,Imane Agmour,Youssef El Foutayeni,Wei-Chiang Hong

doi:10.1155/2021/6619500

Asmaa Idmbarek, Yamna Achik + Show 4 more

Open Access

https://doi.org/10.1155/2021/6619500

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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.

Highlights

The Lotka-Volterra model is one of the primeval predatorprey models to be based on sturdy mathematical principles. It forms the key of many models used nowadays in the analysis of population dynamics [1,2,3,4]
The LotkaVolterra model, unworkable though it is, proposes that uncomplicated predator-prey interactions canister in periodic behavior of the species
In the second work in 2014, Serra [18] considered a mathematical model to describe the interacting behavior of predator and prey. This model is based on the utility functions of the competing

Summary

Introduction

The Lotka-Volterra model is one of the primeval predatorprey models to be based on sturdy mathematical principles. We note that phytoplankton is preyed upon by other sea creatures (ii) In the second phase of the pyramid, we find the zooplankton, which are plankton animal organisms These creatures produce light and energy and rise to the surface at night to feed on phytoplankton and descend during the day to deeper waters. Whales act as a biological pump; they feed on zooplankton In this paper, he assumes that these species are both predatory and prey (v) In the last phase of the pyramid, we find that superpredators like sharks (selachimorphs) are present in all the oceans of the globe and in some large rivers; most sharks breed in the ocean. In the second work in 2014, Serra [18] considered a mathematical model to describe the interacting behavior of predator and prey This model is based on the utility functions of the competing.

Switching-Prey Model

Generalized Nash Equilibrium

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Conclusion and Discussion