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A brief review of predator-prey models for an ecological system with a different type of behaviors

Laxmi Rathour|Lakshmi Narayan Mishra|Ramu Dubey|Kuldeep Singh|Teekam Singh
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2024.09|한국수학논문집 (Korean Journal of Mathematics)|제32권 제3호|pp. 381-406

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참고문헌

키워드

Beddington–DeAngelLotka–Volterrapredator–prey model
주제분류수학

초록

The logistic growth model was developed with a single population in mind. We now analyze the growth of two interdependent populations, moving beyond the one-dimensional model. Interdependence between two species of animals can arise when one (the "prey") acts as a food supply for the other (the "predator"). Predator-prey models are the name given to models of this type. While social scientists are mostly concerned in human communities (where dependency hopefully takes various forms), predator-prey models are interesting for a variety of reasons. Some variations of this model produce limit cycles, an interesting sort of equilibrium that can be found in dynamical systems with two (or more) dimensions. In terms of substance, predator-prey models have a number of beneficial social science applications when the state variables are reinterpreted. This paper provides a quick overview of numerous predator–prey models with various types of behaviours that can be applied to ecological systems, based on a survey of various types of research publications published in the last ten years. The primary source for learning about predator–prey models used in ecological systems is historical research undertaken in various circumstances by various researchers. The review aids in the search for literature that investigates the impact of various parameters on ecological systems. There are also comparisons with traditional models, and the results are double-checked. It can be seen that several older predator–prey models, such as the Beddington–DeAngelis predator–prey model, the stage-structured predator–prey model, and the Lotka–Volterra predator–prey model, are stable and popular among academics. For each of these scenarios, the results are thoroughly checked.

Abstract

The logistic growth model was developed with a single population in mind. We now analyze the growth of two interdependent populations, moving beyond the one-dimensional model. Interdependence between two species of animals can arise when one (the "prey") acts as a food supply for the other (the "predator"). Predator-prey models are the name given to models of this type. While social scientists are mostly concerned in human communities (where dependency hopefully takes various forms), predator-prey models are interesting for a variety of reasons. Some variations of this model produce limit cycles, an interesting sort of equilibrium that can be found in dynamical systems with two (or more) dimensions. In terms of substance, predator-prey models have a number of beneficial social science applications when the state variables are reinterpreted. This paper provides a quick overview of numerous predator–prey models with various types of behaviours that can be applied to ecological systems, based on a survey of various types of research publications published in the last ten years. The primary source for learning about predator–prey models used in ecological systems is historical research undertaken in various circumstances by various researchers. The review aids in the search for literature that investigates the impact of various parameters on ecological systems. There are also comparisons with traditional models, and the results are double-checked. It can be seen that several older predator–prey models, such as the Beddington–DeAngelis predator–prey model, the stage-structured predator–prey model, and the Lotka–Volterra predator–prey model, are stable and popular among academics. For each of these scenarios, the results are thoroughly checked.

참고문헌 (67)

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The Stability of Gauss Model Having Two-Preys and One-PredatorF. Haghighifar, M.H. Rahmani Doust장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2014 · 제17권 제3호Delayed Dynamics of Prey-Predator System with Distinct Functional ResponsesS. Vijaya, V. Madhusudanan경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제2호On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses백헌기경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제4호PHASE ANALYSIS FOR THE PREDATOR-PREY SYSTEMS WITH PREY DENSITY DEPENDENT RESPONSE심성아, 장정욱한국수학교육학회 · 이론수학과 교직수학2018 · 제25권 제4호Dynamics of a discrete ratio-dependent predator-prey system incorporating harvesting박성진, 백헌기, 서정욱, 이상민, 하준수, 현다경영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호Dynamical Behaviors of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response백헌기, 최윤호경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제1호

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