具有Allee效应的离散食饵-捕食模型的分岔分析与混沌控制

IF 0.7 4区数学 Q2 MATHEMATICS

Hacettepe Journal of Mathematics and Statistics Pub Date : 2023-12-31 DOI:10.15672/hujms.1179682

Özlem AK GÜMÜŞ

{"title":"具有Allee效应的离散食饵-捕食模型的分岔分析与混沌控制","authors":"Özlem AK GÜMÜŞ","doi":"10.15672/hujms.1179682","DOIUrl":null,"url":null,"abstract":"In this study, a discrete-time prey-predator model based on the Allee effect is presented. We examine the parametric conditions for local asymptotic stability of fixed points of this model. Furthermore, with the use of the center manifold theorem and bifurcation theory, we analyze the existence and directions of period-doubling and Neimark-Sacker bifurcations. The plots of maximum Lyapunov exponents provide indications of complexity and chaotic behavior. The feedback control approach is presented to stabilize the unstable fixed point. Numerical simulations are performed to support theoretical results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"408 19","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Bifurcation analysis and chaos control of discrete-time prey-predator model with Allee effect\",\"authors\":\"Özlem AK GÜMÜŞ\",\"doi\":\"10.15672/hujms.1179682\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, a discrete-time prey-predator model based on the Allee effect is presented. We examine the parametric conditions for local asymptotic stability of fixed points of this model. Furthermore, with the use of the center manifold theorem and bifurcation theory, we analyze the existence and directions of period-doubling and Neimark-Sacker bifurcations. The plots of maximum Lyapunov exponents provide indications of complexity and chaotic behavior. The feedback control approach is presented to stabilize the unstable fixed point. Numerical simulations are performed to support theoretical results.\",\"PeriodicalId\":55078,\"journal\":{\"name\":\"Hacettepe Journal of Mathematics and Statistics\",\"volume\":\"408 19\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hacettepe Journal of Mathematics and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.15672/hujms.1179682\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1179682","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

本文提出了一种基于Allee效应的离散时间捕食-捕食模型。研究了该模型不动点局部渐近稳定的参数条件。利用中心流形定理和分岔理论，分析了周期加倍分岔和neimmark - sacker分岔的存在性和方向。最大李雅普诺夫指数图提供了复杂性和混沌行为的指示。提出了稳定不稳定不动点的反馈控制方法。数值模拟验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Bifurcation analysis and chaos control of discrete-time prey-predator model with Allee effect

In this study, a discrete-time prey-predator model based on the Allee effect is presented. We examine the parametric conditions for local asymptotic stability of fixed points of this model. Furthermore, with the use of the center manifold theorem and bifurcation theory, we analyze the existence and directions of period-doubling and Neimark-Sacker bifurcations. The plots of maximum Lyapunov exponents provide indications of complexity and chaotic behavior. The feedback control approach is presented to stabilize the unstable fixed point. Numerical simulations are performed to support theoretical results.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.