带条件对称分序 Memristors 的混沌系统的动态分析和滑动模式同步控制

Huaigu Tian, Mingwei Zhao, Jindong Liu, Qiao Wang, Xiong Yu, Zhen Wang
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引用次数: 0

摘要

本文通过电路实现和利用条件对称分数阶忆阻器构建混沌系统,验证了绝对值忆阻器的特性。利用分数阶微积分理论和阿多米分解法(ADM)探讨了分数阶忆阻器系统的动态行为。同时,研究还利用系统参数作为变量,探究了共存的对称吸引子、多个共存的分岔图和李亚普诺夫指数谱(LE)的存在。此外,该系统还展示了一种有趣的现象,即偏移增强(offset boosting),偏移的嵌入可以调整系统吸引子的位置和大小。为了确保这些发现的实际应用性,受整数阶滑动模式理论的启发,设计了一种分数阶滑动模式同步控制方案。通过理论分析和数值模拟,验证了该方案的合理性和可行性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamic Analysis and Sliding Mode Synchronization Control of Chaotic Systems with Conditional Symmetric Fractional-Order Memristors
In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system’s attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation.
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