扩散对具有交叉扩散的退化捕食者-猎物模型的影响

IF 1 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2025-06-04 DOI:10.1007/s10440-025-00732-y

Yu-Xia Wang, Nan Zhang

{"title":"扩散对具有交叉扩散的退化捕食者-猎物模型的影响","authors":"Yu-Xia Wang, Nan Zhang","doi":"10.1007/s10440-025-00732-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we are concerned about the steady state problem of a degenerate predator-prey model with cross-diffusion. First, some properties of principal eigenvalues are deduced. Next, the stability of the semitrivial steady state solutions are obtained. Finally, existence, uniqueness and stability of positive steady state solutions are derived. The result reveals that the diffusion with spatial degeneracy profoundly influences the structure and stability of semitrivial steady state solutions and the coexistence region, which is a strong contrast to the result with no spatial degeneracy.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"197 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Effects of Diffusion on a Degenerate Predator-Prey Model with Cross-Diffusion\",\"authors\":\"Yu-Xia Wang, Nan Zhang\",\"doi\":\"10.1007/s10440-025-00732-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we are concerned about the steady state problem of a degenerate predator-prey model with cross-diffusion. First, some properties of principal eigenvalues are deduced. Next, the stability of the semitrivial steady state solutions are obtained. Finally, existence, uniqueness and stability of positive steady state solutions are derived. The result reveals that the diffusion with spatial degeneracy profoundly influences the structure and stability of semitrivial steady state solutions and the coexistence region, which is a strong contrast to the result with no spatial degeneracy.</p></div>\",\"PeriodicalId\":53132,\"journal\":{\"name\":\"Acta Applicandae Mathematicae\",\"volume\":\"197 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Applicandae Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10440-025-00732-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Applicandae Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10440-025-00732-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了一类具有交叉扩散的退化捕食-食饵模型的稳态问题。首先，推导了主特征值的一些性质。其次，得到了半平凡稳态解的稳定性。最后，导出了正稳态解的存在唯一性和稳定性。结果表明，具有空间简并的扩散对半平凡稳态解和共存区域的结构和稳定性产生了深刻的影响，这与没有空间简并的结果形成了强烈的对比。

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

Effects of Diffusion on a Degenerate Predator-Prey Model with Cross-Diffusion

In this paper, we are concerned about the steady state problem of a degenerate predator-prey model with cross-diffusion. First, some properties of principal eigenvalues are deduced. Next, the stability of the semitrivial steady state solutions are obtained. Finally, existence, uniqueness and stability of positive steady state solutions are derived. The result reveals that the diffusion with spatial degeneracy profoundly influences the structure and stability of semitrivial steady state solutions and the coexistence region, which is a strong contrast to the result with no spatial degeneracy.

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 Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.