Dynamics analysis and predefined-time sliding mode synchronization of multi-scroll systems based on a single memristor model

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Shaohui Yan, Xinyu Wu, Jiawei Jiang
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引用次数: 0

Abstract

To overcome the limitations of conventional designs for memristive multi-scroll chaotic systems, this paper introduces a novel memristor that relies solely on a single memristor function and a single state variable function to generate both odd and even numbers of double-scroll attractors. This design not only simplifies the memristor structure but also offers a new approach to constructing multi-scroll chaotic systems. The proposed memristor is integrate into a modified Sprott-C system to develop the one-dimensional memristive multi-scroll Sprott-C systems (1D-MMSCS), two-dimensional memristive multi-scroll Sprott-C systems (2D-MMSCS), and the three-dimensional memristive multi-scroll Sprott-C systems (3D-MMSCS). The complex dynamics of these memristive multi-scroll systems are analyzed using equilibrium points, Poincaré maps, bifurcation diagrams, and Lyapunov exponents. Interestingly, the constructed MMSCS exhibits extreme multi-stability, indicating its high sensitivity to initial conditions and enhanced unpredictability. To verify the practical feasibility of the system, it is developed a digital hardware platform based on a Field-Programmable Gate Array (FPGA) and successfully implemented both the 1D-MMSCS and 2D-MMSCS. Finally, leveraging Lyapunov stability theory and predefined-time stability theory, a novel predefined-time sliding mode control scheme (PTSMS) is proposed. This scheme is applied to achieve synchronization in the more complex 3D-MMSCS. Simulation results confirm that the proposed method ensures rapid synchronization and exhibits strong robustness against internal uncertainties and external disturbances.
基于单一忆阻器模型的多涡旋系统动力学分析及预定义时间滑模同步
为了克服传统记忆多涡旋混沌系统设计的局限性,本文介绍了一种仅依靠单一忆阻函数和单一状态变量函数产生奇数和偶数双涡旋吸引子的新型忆阻器。该设计不仅简化了忆阻器结构,而且为构建多涡旋混沌系统提供了新的途径。将所提出的忆阻器集成到改进的Sprott-C系统中,开发出一维忆阻多卷Sprott-C系统(1D-MMSCS)、二维忆阻多卷Sprott-C系统(2D-MMSCS)和三维忆阻多卷Sprott-C系统(3D-MMSCS)。这些记忆多涡旋系统的复杂动力学分析使用平衡点,庞加莱图,分岔图,和李亚普诺夫指数。有趣的是,构建的MMSCS表现出极端的多稳定性,表明其对初始条件的高灵敏度和增强的不可预测性。为了验证该系统的实际可行性,开发了基于现场可编程门阵列(FPGA)的数字硬件平台,并成功实现了1D-MMSCS和2D-MMSCS。最后,利用李雅普诺夫稳定性理论和预定义时间稳定性理论,提出了一种新的预定义时间滑模控制方案。该方案应用于更复杂的3D-MMSCS中实现同步。仿真结果表明,该方法能够保证系统的快速同步,并对系统内部不确定性和外部干扰具有较强的鲁棒性。
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
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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