多重延迟对浮游生物-鱼类系统动力学的影响

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-25 DOI:10.1002/mma.11158

Renxiang Shi

{"title":"多重延迟对浮游生物-鱼类系统动力学的影响","authors":"Renxiang Shi","doi":"10.1002/mma.11158","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This paper studies the dynamics of a plankton-fish system with three delays. First, we prove the positivity and boundedness of solutions. Then, under three cases: one delay, two delays, and three delays, we discuss the influence of multiple delays on the dynamics by theoretical analysis and simulation. At last, in absence and presence of delays, we give the influence of fear effect on the dynamics by simulations. Our results reveal that both delays and fear effect bring rich dynamics for plankton-fish system, such as periodic oscillation and chaos.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14026-14040"},"PeriodicalIF":1.8000,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Influence of Multiple Delays on the Dynamics of Plankton-Fish System\",\"authors\":\"Renxiang Shi\",\"doi\":\"10.1002/mma.11158\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>This paper studies the dynamics of a plankton-fish system with three delays. First, we prove the positivity and boundedness of solutions. Then, under three cases: one delay, two delays, and three delays, we discuss the influence of multiple delays on the dynamics by theoretical analysis and simulation. At last, in absence and presence of delays, we give the influence of fear effect on the dynamics by simulations. Our results reveal that both delays and fear effect bring rich dynamics for plankton-fish system, such as periodic oscillation and chaos.</p>\\n </div>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"48 15\",\"pages\":\"14026-14040\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2025-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.11158\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.11158","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了具有三时滞的浮游生物-鱼类系统的动力学问题。首先证明了解的正性和有界性。然后，在单延时、双延时和三延时三种情况下，通过理论分析和仿真，讨论了多延时对系统动力学的影响。最后，在无延迟和有延迟的情况下，通过仿真给出了恐惧效应对动力学的影响。研究结果表明，延迟效应和恐惧效应都为浮游生物-鱼类系统带来了丰富的动力学特征，如周期振荡和混沌。

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

The Influence of Multiple Delays on the Dynamics of Plankton-Fish System

This paper studies the dynamics of a plankton-fish system with three delays. First, we prove the positivity and boundedness of solutions. Then, under three cases: one delay, two delays, and three delays, we discuss the influence of multiple delays on the dynamics by theoretical analysis and simulation. At last, in absence and presence of delays, we give the influence of fear effect on the dynamics by simulations. Our results reveal that both delays and fear effect bring rich dynamics for plankton-fish system, such as periodic oscillation and chaos.

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.