{"title":"Traveling Waves of Modified Leslie-Gower Predator-prey Systems","authors":"Hongliang Li, Min Zhao, R. Yuan","doi":"10.1142/s1793524523501073","DOIUrl":null,"url":null,"abstract":"The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity information on wave profile based on the asymptotic behavior at negative infinite. Finally, our results are applied to modified Leslie-Gower system with Holling II type or Lotka-Volterra type, and then a novel Lyapunov function is constructed for the latter, which further enhances our results. Meanwhile, some numerical simulations are carried to support our results.","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"17 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Biomathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793524523501073","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICAL & COMPUTATIONAL BIOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity information on wave profile based on the asymptotic behavior at negative infinite. Finally, our results are applied to modified Leslie-Gower system with Holling II type or Lotka-Volterra type, and then a novel Lyapunov function is constructed for the latter, which further enhances our results. Meanwhile, some numerical simulations are carried to support our results.
本文的主题是修正的莱斯利-高尔反应扩散捕食者-猎物系统中的扩散现象。我们主要研究了两种不同类型行波的存在。具体来说，我们借助上解和下解法，通过构造不同的、合适的李亚普诺夫函数，确定了连接猎物存在状态和共存状态或猎物存在状态和无猎物状态的行波的存在性。此外，对于连接有猎物状态和无猎物状态的行波，我们根据负无限时的渐近行为获得了更多关于波形的单调性信息。最后，我们将结果应用于霍林 II 型或洛特卡-伏特拉型的修正莱斯利-高尔系统，并为后者构建了一个新的 Lyapunov 函数，从而进一步增强了我们的结果。同时，我们还进行了一些数值模拟来支持我们的结果。
期刊介绍：
The goal of this journal is to present the latest achievements in biomathematics, facilitate international academic exchanges and promote the development of biomathematics. Its research fields include mathematical ecology, infectious disease dynamical system, biostatistics and bioinformatics.
Only original papers will be considered. Submission of a manuscript indicates a tacit understanding that the paper is not actively under consideration for publication with other journals. As submission and reviewing processes are handled electronically whenever possible, the journal promises rapid publication of articles.
The International Journal of Biomathematics is published bimonthly.
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