{"title":"Analysis of the Dynamics of Solutions for Hybrid Difference\nLotka–Volterra Systems","authors":"A. V. Platonov","doi":"10.1134/S199047892404015X","DOIUrl":null,"url":null,"abstract":"<p> A difference system of the Lotka–Volterra type is considered. It is assumed that this\nsystem can operate both in some program and perturbed modes. The restrictions on the time of\nthe system’s stay in these modes, providing the desired dynamical behavior, are investigated. In\nparticular, the conditions of the ultimate boundedness of solutions and the permanence of the\nsystem are obtained. The direct Lyapunov method is used, and different Lyapunov functions are\nconstructed in different parts of the state space. The sizes of the domain of permissible initial\nvalues of solutions and the domain of the ultimate bound of solutions corresponding to the\nrequired dynamics of the system are estimated. Constraints are set on the size of the digitization\nstep of the system.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"812 - 823"},"PeriodicalIF":0.5800,"publicationDate":"2025-07-11","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/S199047892404015X","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
A difference system of the Lotka–Volterra type is considered. It is assumed that this
system can operate both in some program and perturbed modes. The restrictions on the time of
the system’s stay in these modes, providing the desired dynamical behavior, are investigated. In
particular, the conditions of the ultimate boundedness of solutions and the permanence of the
system are obtained. The direct Lyapunov method is used, and different Lyapunov functions are
constructed in different parts of the state space. The sizes of the domain of permissible initial
values of solutions and the domain of the ultimate bound of solutions corresponding to the
required dynamics of the system are estimated. Constraints are set on the size of the digitization
step of the system.
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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