{"title":"Dynamical analysis of a discrete-time plant–herbivore model","authors":"M. Y. Hamada","doi":"10.1007/s40065-023-00442-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a discrete-time model of a plant–herbivore system is qualitatively analyzed using difference equations to describe population dynamics over time. The goal is to examine how the model behaves under varying parameter values and initial conditions. Results reveal that the model exhibits diverse dynamical behaviors such as stable equilibria, period-doubling cascade, and chaotic attractors. The analysis indicates that changes in crucial parameters greatly affect the system’s dynamics. This study offers crucial insights into plant–herbivore systems and highlights the value of qualitative analysis in comprehending intricate ecological systems.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-023-00442-z.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-023-00442-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a discrete-time model of a plant–herbivore system is qualitatively analyzed using difference equations to describe population dynamics over time. The goal is to examine how the model behaves under varying parameter values and initial conditions. Results reveal that the model exhibits diverse dynamical behaviors such as stable equilibria, period-doubling cascade, and chaotic attractors. The analysis indicates that changes in crucial parameters greatly affect the system’s dynamics. This study offers crucial insights into plant–herbivore systems and highlights the value of qualitative analysis in comprehending intricate ecological systems.
期刊介绍：
The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics.
Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.
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