Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-12-15 DOI:10.3390/axioms12121125

Jindong Liu, Huaigu Tian, Zhen Wang, Yan Guan, Zelin Cao

引用次数: 0

Abstract

In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix.

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新型 RLCM 分数阶晶闸管电路系统的动态分析与错位投影同步化

本文建立了一种简单而新颖的分数阶忆阻器电路，该电路仅包含电阻、电感、电容和忆阻器。利用分数微积分理论和 Adomian 数值算法，研究了系统在不同阶数、参数和初始忆阻器值的一维和二维参数变化下的特殊分岔、混沌退化、C0 和频谱熵（SE）复杂度。同时，为了更好地利用分数阶忆阻器系统在通信和安全领域的应用，提出了一种分数阶系统的错位投影同步方案，克服了构建分数阶系统的李亚普诺夫函数来证明稳定性和设计拉普拉斯变换矩阵控制器的缺点。

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

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.