Korean Journal of Mathematics

  • 제32권3호
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  • Pages.381-406
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  • 2024
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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A BRIEF REVIEW OF PREDATOR-PREY MODELS FOR AN ECOLOGICAL SYSTEM WITH A DIFFERENT TYPE OF BEHAVIORS

  • Kuldeep Singh (Department of Mathematics, J.C. Bose University of Science and Technology, YMCA) ;
  • Teekam Singh (Department of Mathematics, Graphic Era (Deemed to be) University) ;
  • Lakshmi Narayan Mishra (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology) ;
  • Ramu Dubey (Department of Mathematics, J.C. Bose University of Science and Technology, YMCA) ;
  • Laxmi Rathour (Department of Mathematics, National Institute of Technology)
  • 투고 : 2023.12.12
  • 심사 : 2024.09.02
  • 발행 : 2024.09.30
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⟨ 이전 논문 다음 논문 ⟩

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.

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참고문헌

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