Dynamics analysis and fractional-order nonlinearity system via memristor-based Chua oscillator

IF 1.9 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Pramana Pub Date : 2023-07-12 DOI:10.1007/s12043-023-02590-5

S Sabarathinam, Viktor Papov, Zi-Peng Wang, R Vadivel, NALLAPPAN Gunasekaran

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引用次数: 0

Abstract

This article discusses the utilisation of a Chua oscillator with a memristor to produce chaos with minimal nonlinearity. The memristor, a device that changes its flux or charges over time, has its nonlinear strength altered fractionally to determine the lowest-order memristor nonlinearity for generating chaos. An experimental analog circuit in real-time has been constructed. A linear parameter varying (LPV) approach, incorporating a suitable Lyapunov functional (LK) method, has been introduced to find new sufficient conditions for the robust stability of the resulting closed-loop system through linear matrix inequalities (LMIs). By observing the behaviour of the system without control, it is possible to understand the basic characteristics of chaotic oscillations and how they are affected by changes in the fractional order. These results can then be used as a starting point to study the effectiveness of various control techniques, such as feedback control, in reducing chaos and stabilising the system of this article. The efficiency of the cost-function-based control scheme is evaluated using the simulation results and relevant applications are addressed.

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基于忆阻器的蔡振荡器的分数阶非线性系统动力学分析

本文讨论了利用带忆阻器的蔡氏振荡器产生非线性最小的混沌。忆阻器是一种随时间改变其磁通或电荷的器件，其非线性强度发生了微小的变化，以确定产生混沌的最低阶忆阻器非线性。构建了一个实时的实验模拟电路。采用线性变参数(LPV)方法，结合合适的Lyapunov泛函(LK)方法，通过线性矩阵不等式(lmi)找到闭环系统鲁棒稳定性的新充分条件。通过观察无控制系统的行为，可以了解混沌振荡的基本特征以及它们如何受到分数阶变化的影响。这些结果可以作为研究各种控制技术(如反馈控制)在减少混沌和稳定本文系统方面的有效性的起点。利用仿真结果评价了基于成本函数的控制方案的有效性，并讨论了相关应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Pramana 物理-物理：综合

CiteScore

3.60

自引率

7.10%

发文量

206

审稿时长

3 months

期刊介绍： Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.