Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives
Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives
复制标题
DOI：
10.1016/j.chaos.2019.06.037
复制
发表时间：
2019-10-01
影响因子：
7.8
通讯作者：
Pindza, Edson
中科院分区：
文献类型：
--
作者：
Owolabi, Kolade M.;Pindza, Edson
本文考虑了分数式反应扩散系统的数学分析和数值处理。在该模型中，一阶时间导数采用 Atangana-Baleanu 和 Caputo-Fabrizio 导数的分数情况进行建模，其公式基于著名的 Mittag-Leffler 核。检查主系统的稳定性，以确保在对完整模型进行数值模拟时正确选择参数。采用新颖的 Adam-Bashforth 数值方案来逼近这些算子。这项工作中引入的技术的适用性和适用性通过物种在一维和二维的进化来证明。获得的结果表明，分数阶导数建模可以产生一些图灵模式。 (C) 2019 Elsevier Ltd. 保留所有权利。
This paper considers mathematical analysis and numerical treatment for fractional reaction-diffusion system. In the model, the first-order time derivatives are modelled with the fractional cases of both the Atangana-Baleanu and Caputo-Fabrizio derivatives whose formulations are based on the notable Mittag-Leffler kernel. The main system is examined for stability to ensure the right choice of parameters when numerically simulating the full model. The novel Adam-Bashforth numerical scheme is employed for the approximation of these operators. Applicability and suitability of the techniques introduced in this work is justified via the evolution of the species in one and two dimensions. The results obtained show that modelling with fractional derivative can give rise to some Turing patterns. (C) 2019 Elsevier Ltd. All rights reserved.