{"title":"扩散霍林-坦纳猎物-捕食者模型的对称性和精确解","authors":"Roman Cherniha, Vasyl' Davydovych","doi":"arxiv-2402.19098","DOIUrl":null,"url":null,"abstract":"We consider the classical Holling-Tanner model extended on 1D space by\nintroducing the diffusion term. Making a reasonable simplification, the\ndiffusive Holling-Tanner system is studied by means of symmetry based methods.\nLie and Q-conditional (nonclassical) symmetries are identified. The symmetries\nobtained are applied for finding a wide range of exact solutions, their\nproperties are studied and a possible biological interpretation is proposed. 3D\nplots of the most interesting solutions are drown as well.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Symmetries and exact solutions of the diffusive Holling-Tanner prey-predator model\",\"authors\":\"Roman Cherniha, Vasyl' Davydovych\",\"doi\":\"arxiv-2402.19098\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the classical Holling-Tanner model extended on 1D space by\\nintroducing the diffusion term. Making a reasonable simplification, the\\ndiffusive Holling-Tanner system is studied by means of symmetry based methods.\\nLie and Q-conditional (nonclassical) symmetries are identified. The symmetries\\nobtained are applied for finding a wide range of exact solutions, their\\nproperties are studied and a possible biological interpretation is proposed. 3D\\nplots of the most interesting solutions are drown as well.\",\"PeriodicalId\":501275,\"journal\":{\"name\":\"arXiv - PHYS - Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2402.19098\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2402.19098","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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.
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