一类具有两个时间延迟的捕食者--猎物模型的动态行为

IF 2.3 3区工程技术 Q2 MECHANICS

Acta Mechanica Pub Date : 2024-10-01 DOI:10.1007/s00707-024-04111-w

Youhua Qian, Meirong Ren, Haolan Wang

{"title":"一类具有两个时间延迟的捕食者--猎物模型的动态行为","authors":"Youhua Qian, Meirong Ren, Haolan Wang","doi":"10.1007/s00707-024-04111-w","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, three modified Leslie–Gower predator–prey models with two time delays are considered based on the original Leslie–Gower predator–prey model. Taking the time delay as a bifurcation parameter, when Hopf bifurcation occurs, the critical value corresponding to time delay is obtained. By using normal form theory and central manifold argument, the direction of Hopf bifurcation and the stability of bifurcation periodic solution can be determined. The time delay affects the stability of the positive equilibria. When the time delay exceeds the critical value, the positive equilibria change from stable to unstable and bifurcate out a set of periodic solutions. Finally, numerical simulation is performed to support theoretical analysis.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"235 12","pages":"7453 - 7473"},"PeriodicalIF":2.3000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamic behavior of a class of predator–prey model with two time delays\",\"authors\":\"Youhua Qian, Meirong Ren, Haolan Wang\",\"doi\":\"10.1007/s00707-024-04111-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, three modified Leslie–Gower predator–prey models with two time delays are considered based on the original Leslie–Gower predator–prey model. Taking the time delay as a bifurcation parameter, when Hopf bifurcation occurs, the critical value corresponding to time delay is obtained. By using normal form theory and central manifold argument, the direction of Hopf bifurcation and the stability of bifurcation periodic solution can be determined. The time delay affects the stability of the positive equilibria. When the time delay exceeds the critical value, the positive equilibria change from stable to unstable and bifurcate out a set of periodic solutions. Finally, numerical simulation is performed to support theoretical analysis.</p></div>\",\"PeriodicalId\":456,\"journal\":{\"name\":\"Acta Mechanica\",\"volume\":\"235 12\",\"pages\":\"7453 - 7473\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mechanica\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00707-024-04111-w\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-024-04111-w","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}

引用次数: 0

摘要

本文在原莱斯利-高尔捕食者-猎物模型的基础上，考虑了三个具有两个时间延迟的修正莱斯利-高尔捕食者-猎物模型。将时间延迟作为分岔参数，当发生霍普夫分岔时，得到时间延迟对应的临界值。利用正则表达式理论和中心流形论证，可以确定霍普夫分岔的方向和分岔周期解的稳定性。时间延迟会影响正平衡的稳定性。当时间延迟超过临界值时，正平衡态由稳定变为不稳定，并分岔出一组周期解。最后，进行了数值模拟以支持理论分析。

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

Dynamic behavior of a class of predator–prey model with two time delays

In this paper, three modified Leslie–Gower predator–prey models with two time delays are considered based on the original Leslie–Gower predator–prey model. Taking the time delay as a bifurcation parameter, when Hopf bifurcation occurs, the critical value corresponding to time delay is obtained. By using normal form theory and central manifold argument, the direction of Hopf bifurcation and the stability of bifurcation periodic solution can be determined. The time delay affects the stability of the positive equilibria. When the time delay exceeds the critical value, the positive equilibria change from stable to unstable and bifurcate out a set of periodic solutions. Finally, numerical simulation is performed to support theoretical analysis.

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

Acta Mechanica 物理-力学

CiteScore

4.30

自引率

14.80%

发文量

292

审稿时长

6.9 months

期刊介绍： Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.