Introducing memristors into the traditional chaotic system can generate multiscroll chaotic attractors, expanding possibilities for information processing and chaotic applications. This paper first proposes a novel multi-segment memristor model based on a multi-segment linear function. Then, based on the Sprott-B system, one-directional memristive multiscroll chaotic attractors (1D-MMSCAs), 2D-MMSCAs, and 3D-MMSCAs are produced separately, with different numbers of novel memristors introduced. The dynamic behavior of the MMSCAs is analyzed in terms of equilibrium points, Lyapunov exponents and bifurcations, coexisting attractors, and complexity. Lyapunov exponent and bifurcation analysis reveal rich dynamic behavior of the MMSCAs, including period-doubling bifurcations, bursts of chaos, and transient of chaos. The MMSCAs exhibit dynamic phenomena such as coexisting attractors, multistability, and super multistability under different initial conditions. Furthermore, the existence and feasibility of the MMSCAs are verified through circuit simulation. Coexisting attractors generation circuits that can change the initial values of arbitrary state variables are designed. Using an improved Euler algorithm and the STM32 microcontroller, the MMSCAs are digitally implemented, expanding the application scope. Comparative results with other multi-scroll chaotic attractors (MSCAs) demonstrate the advantages of the proposed MMSCAs, including controllable scroll number and direction, simple implementation circuits, and rich dynamic behavior. Finally, the MMSCAs are applied to finite-time synchronization. Simulation results show that the two proposed synchronization schemes in this paper require less time to achieve complete synchronization compared to other synchronization schemes. This characteristic enhances the efficiency and practicality of the proposed synchronization strategy in real-world applications.

中文翻译：

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基于新型多段忆阻器的多涡旋混沌吸引子的设计与应用

在传统混沌系统中引入忆阻器可以产生多涡旋混沌吸引子，拓展了信息处理和混沌应用的可能性。本文首先提出了一种基于多段线性函数的新型多段忆阻器模型。然后，基于Sprott-B系统，分别制备了单向忆阻多涡卷混沌吸引子（1D-MMSCA）、2D-MMSCA和3D-MMSCA，并引入了不同数量的新型忆阻器。MMSCA 的动态行为根据平衡点、Lyapunov 指数和分岔、共存吸引子和复杂性进行了分析。Lyapunov 指数和分岔分析揭示了 MMSCA 丰富的动态行为，包括倍周期分岔、混沌爆发和混沌瞬态。MMSCA在不同初始条件下表现出共存吸引子、多稳定性和超多稳定性等动态现象。此外，通过电路仿真验证了MMSCA的存在性和可行性。设计了可以改变任意状态变量初始值的共存吸引子生成电路。采用改进的欧拉算法和STM32微控制器，对MMSCA进行数字化实现，扩大了应用范围。与其他多滚动混沌吸引器（MSCA）的比较结果证明了所提出的MMSCA的优点，包括可控滚动数量和方向、简单的实现电路和丰富的动态行为。最后，将MMSCA应用于有限时间同步。仿真结果表明，与其他同步方案相比，本文提出的两种同步方案需要更少的时间来实现完全同步。这一特性提高了所提出的同步策略在实际应用中的效率和实用性。