{"title":"扩散Holling-Tanner捕食-捕食模型的对称性和精确解","authors":"Roman Cherniha, Vasyl’ Davydovych","doi":"10.1007/s10440-023-00600-7","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the classical Holling–Tanner model extended on 1D space by introducing the diffusion term. Making a reasonable simplification, the diffusive Holling–Tanner system is studied by means of symmetry based methods. Lie and <span>\\(Q\\)</span>-conditional (nonclassical) symmetries are identified. The symmetries obtained are applied for finding a wide range of exact solutions, their properties are studied and a possible biological interpretation is proposed. 3D plots of the most interesting solutions are drown as well.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-023-00600-7.pdf","citationCount":"0","resultStr":"{\"title\":\"Symmetries and Exact Solutions of the Diffusive Holling–Tanner Prey-Predator Model\",\"authors\":\"Roman Cherniha, Vasyl’ Davydovych\",\"doi\":\"10.1007/s10440-023-00600-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the classical Holling–Tanner model extended on 1D space by introducing the diffusion term. Making a reasonable simplification, the diffusive Holling–Tanner system is studied by means of symmetry based methods. Lie and <span>\\\\(Q\\\\)</span>-conditional (nonclassical) symmetries are identified. The symmetries obtained are applied for finding a wide range of exact solutions, their properties are studied and a possible biological interpretation is proposed. 3D plots of the most interesting solutions are drown as well.</p></div>\",\"PeriodicalId\":53132,\"journal\":{\"name\":\"Acta Applicandae Mathematicae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10440-023-00600-7.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Applicandae Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10440-023-00600-7\",\"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/s10440-023-00600-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Symmetries and Exact Solutions of the Diffusive Holling–Tanner Prey-Predator Model
We consider the classical Holling–Tanner model extended on 1D space by introducing the diffusion term. Making a reasonable simplification, the diffusive Holling–Tanner system is studied by means of symmetry based methods. Lie and \(Q\)-conditional (nonclassical) symmetries are identified. The symmetries obtained are applied for finding a wide range of exact solutions, their properties are studied and a possible biological interpretation is proposed. 3D plots of the most interesting solutions are drown as well.
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.