具有非线性边界条件的反应-扩散-平流系统的动力学特性

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI:10.1142/s0218127423501936

Chenyuan Tian, Shangjiang Guo

{"title":"具有非线性边界条件的反应-扩散-平流系统的动力学特性","authors":"Chenyuan Tian, Shangjiang Guo","doi":"10.1142/s0218127423501936","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a single-species reaction–diffusion–advection population model with nonlinear boundary condition in heterogenous space. We not only investigate the existence, nonexistence and stability of positive steady-state solutions through a linear elliptic eigenvalue problem by means of variational approach, but also verify the existence of steady-state bifurcations at zero solution through Crandall and Robinowitz bifurcation theory and discuss the stability of bifurcations, which can lead to Allee effect when the bifurcation is subcritical.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 3","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamics of a Reaction–Diffusion–Advection System with Nonlinear Boundary Conditions\",\"authors\":\"Chenyuan Tian, Shangjiang Guo\",\"doi\":\"10.1142/s0218127423501936\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider a single-species reaction–diffusion–advection population model with nonlinear boundary condition in heterogenous space. We not only investigate the existence, nonexistence and stability of positive steady-state solutions through a linear elliptic eigenvalue problem by means of variational approach, but also verify the existence of steady-state bifurcations at zero solution through Crandall and Robinowitz bifurcation theory and discuss the stability of bifurcations, which can lead to Allee effect when the bifurcation is subcritical.\",\"PeriodicalId\":50337,\"journal\":{\"name\":\"International Journal of Bifurcation and Chaos\",\"volume\":\" 3\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Bifurcation and Chaos\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218127423501936\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Bifurcation and Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218127423501936","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

本文考虑了异质空间中具有非线性边界条件的单物种反应-扩散-对流种群模型。我们不仅通过线性椭圆特征值问题，利用变分法研究了正稳态解的存在、不存在和稳定性，还通过 Crandall 和 Robinowitz 分岔理论验证了零解处稳态分岔的存在性，并讨论了分岔的稳定性，当分岔为亚临界时，可能会导致阿利效应。

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

Dynamics of a Reaction–Diffusion–Advection System with Nonlinear Boundary Conditions

In this paper, we consider a single-species reaction–diffusion–advection population model with nonlinear boundary condition in heterogenous space. We not only investigate the existence, nonexistence and stability of positive steady-state solutions through a linear elliptic eigenvalue problem by means of variational approach, but also verify the existence of steady-state bifurcations at zero solution through Crandall and Robinowitz bifurcation theory and discuss the stability of bifurcations, which can lead to Allee effect when the bifurcation is subcritical.

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

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.