{"title":"Fractal dynamics of solution moments for the KPP–Fisher equation","authors":"A. V. Shapovalov, S. A. Siniukov","doi":"10.1007/s11182-024-03319-6","DOIUrl":null,"url":null,"abstract":"<div><p>The paper focuses on the KPP–Fisher equation (named after Andrey Kolmogorov, Ivan Petrovskii, Nikolai Piskunov and Ronald Fisher) with non-local competitive losses and fractal time derivative which is considered in terms of F<sup>α</sup>-calculus on the Cantor set dimension 0 < α < 1. A dynamic system with the fractal time derivative relating to the moments not higher than the second-order for the KPP–Fisher equation, is deduced in the semiclassical approximation with respect to the small diffusion parameter in the class of trajectory-concentrated functions. An example is given to the dynamic system of solution moments constructed and explored for various values of α parameter.</p></div>","PeriodicalId":770,"journal":{"name":"Russian Physics Journal","volume":"67 11","pages":"1827 - 1837"},"PeriodicalIF":0.4000,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Physics Journal","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11182-024-03319-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The paper focuses on the KPP–Fisher equation (named after Andrey Kolmogorov, Ivan Petrovskii, Nikolai Piskunov and Ronald Fisher) with non-local competitive losses and fractal time derivative which is considered in terms of Fα-calculus on the Cantor set dimension 0 < α < 1. A dynamic system with the fractal time derivative relating to the moments not higher than the second-order for the KPP–Fisher equation, is deduced in the semiclassical approximation with respect to the small diffusion parameter in the class of trajectory-concentrated functions. An example is given to the dynamic system of solution moments constructed and explored for various values of α parameter.
期刊介绍：
Russian Physics Journal covers the broad spectrum of specialized research in applied physics, with emphasis on work with practical applications in solid-state physics, optics, and magnetism. Particularly interesting results are reported in connection with: electroluminescence and crystal phospors; semiconductors; phase transformations in solids; superconductivity; properties of thin films; and magnetomechanical phenomena.
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