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基于具有分数阶导数的分形分数阶幂律核的电路设计的混沌系统动力学的乌拉姆稳定性。

Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel.

机构信息

Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, 25000, Pakistan.

Department of Mathematics and Physics, University of Campania "Luigi Vanvitelli", 81100, Caserta, Italy.

出版信息

Sci Rep. 2023 Mar 28;13(1):5043. doi: 10.1038/s41598-023-32099-1.

DOI:10.1038/s41598-023-32099-1
PMID:36977727
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10050208/
Abstract

In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.

摘要

在本文中，使用新开发的具有幂律核的分形分数导数来分析基于电路设计的混沌系统的动力学。该问题采用经典阶非线性、耦合常微分方程建模，然后通过具有幂律核的分形分数导数进行推广。此外，还计算了该系统的几个理论分析，如模型平衡点、存在性、唯一性和 Ulam 稳定性。然后使用 MATLAB 软件通过数值技术分析高度非线性的分形分数阶系统。图形解以二维图和三维相图表示，并在讨论部分详细解释，同时从当前研究中得出一些结论。值得注意的是，分形分数微分算子可以通过调整分形和分数参数，快速将混沌系统的动力学收敛到其静态平衡。

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