具有瓦特型功能响应的脉冲控制捕食系统的复杂动态行为

Pub Date : 2016-09-23 DOI:10.5666/KMJ.2016.56.3.831

H. Baek

{"title":"具有瓦特型功能响应的脉冲控制捕食系统的复杂动态行为","authors":"H. Baek","doi":"10.5666/KMJ.2016.56.3.831","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Complex Dynamic Behaviors of an Impulsively Controlled Predator-prey System with Watt-type Functional Response\",\"authors\":\"H. Baek\",\"doi\":\"10.5666/KMJ.2016.56.3.831\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2016-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5666/KMJ.2016.56.3.831\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5666/KMJ.2016.56.3.831","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

本文考虑一个具有瓦特型函数响应和脉冲控制的离散捕食者-猎物系统。首先利用Floquet理论找到了系统无猎物正周期解稳定的充分条件，然后证明了系统的有界性。此外，还得到了系统持久的一个条件。最后，我们举例说明了一些数值例子来证实我们的理论结果，并通过数值模拟显示了系统的一些解的分岔图和轨迹，表明脉冲控制可以产生各种动态行为。

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

Complex Dynamic Behaviors of an Impulsively Controlled Predator-prey System with Watt-type Functional Response

In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.

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