{"title":"Modeling Competition between Populations with Multi-Taxis","authors":"A. V. Budyansky, V. G. Tsybulin","doi":"10.1134/S1990478923030043","DOIUrl":null,"url":null,"abstract":"<p> We study a mathematical model of competition between two populations described by a\nsystem of nonlinear differential reaction–diffusion–advection equations. The taxis is introduced to\nmodel the heterogeneity of the total resource and the nonuniform distribution of both species. We\nanalyze the role of the taxis in the area occupancy. The maps of migration parameters\ncorresponding to various variants of competitive exclusion and coexistence of species are\ncalculated. Using the theory of cosymmetry, we find parametric relations under which\nmultistability arises. In a computational experiment, population scenarios with a violation of\ncosymmetry were studied.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"498 - 506"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923030043","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We study a mathematical model of competition between two populations described by a
system of nonlinear differential reaction–diffusion–advection equations. The taxis is introduced to
model the heterogeneity of the total resource and the nonuniform distribution of both species. We
analyze the role of the taxis in the area occupancy. The maps of migration parameters
corresponding to various variants of competitive exclusion and coexistence of species are
calculated. Using the theory of cosymmetry, we find parametric relations under which
multistability arises. In a computational experiment, population scenarios with a violation of
cosymmetry were studied.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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