KPP-Fisher方程解矩的分形动力学

IF 0.4 4区物理与天体物理 Q4 PHYSICS, MULTIDISCIPLINARY

Russian Physics Journal Pub Date : 2025-02-07 DOI:10.1007/s11182-024-03319-6

A. V. Shapovalov, S. A. Siniukov

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引用次数: 0

摘要

本文主要研究具有非局部竞争损失和分形时间导数的KPP-Fisher方程（以Andrey Kolmogorov， Ivan Petrovskii， Nikolai Piskunov和Ronald Fisher命名），该方程在康托集维数0 <； α <； 1上用f α-演算来考虑。对轨迹集中函数类的小扩散参数，用半经典近似推导出了KPP-Fisher方程的分形时间导数不高于二阶矩的动力系统。给出了α参数不同取值时构造和探索的解矩动态系统的实例。

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Fractal dynamics of solution moments for the KPP–Fisher equation

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^α-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.

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来源期刊

Russian Physics Journal PHYSICS, MULTIDISCIPLINARY-

CiteScore

1.00

自引率

50.00%

发文量

208

审稿时长

3-6 weeks

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.