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A Multi-Scroll Memristive Chaotic System via Fractal Process

机译：通过分形过程多滚动忆混系统

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Fractal theory is a leading and important branch of nonlinear science, which has been widely studied in many fields in the past few decades. Memristor is a nanoscale element with low power consumption and high integration, when it works as the nonlinear part in a chaotic system, the complexity of the chaotic system will be enhanced. Compared with single-scroll chaotic attractor, multi-scroll chaotic attractor have higher complexity and better adaptability. In this paper, the fractal process is applied to a known memristive chaotic system, which can generate multi-scroll chaotic attractor. At first, a fractal iteration is applied to the memristive chaotic system to generate new chaotic attractor. Secondly, the multi-scroll chaotic system is obtained by combining the Julia fractal and memristive chaotic system. And by changing a complex constant in the fractal process, a fractal graph with different shapes is obtained, which can also be used to generate different chaotic attractors in the generating multi-scroll memristive chaotic system. Compared with other multi-scroll chaotic attractors, the proposed multi-scroll chaotic attractors are easier to adjust the number of the scrolls. It can be seen from the simulation diagram that the size of the system phase diagram becomes smaller and smaller as the number of scrolls increases. The results show that the new system has a lot of dynamic characteristics.
机译：分形理论是非线性科学的主要和重要分支，在过去几十年中已广泛研究过许多领域。忆阻器是具有低功耗和高集成度的纳米级元素，当它作为混沌系统中的非线性部分时，混沌系统的复杂性将得到增强。与单卷轴混沌吸引子相比，多滚动混沌吸引子具有更高的复杂性和更好的适应性。在本文中，分形过程应用于已知的忆振混沌系统，其可以产生多涡旋混沌吸引子。首先，将分形迭代应用于忆反混沌系统以产生新的混沌吸引子。其次，通过组合朱莉娅分形和忆内混沌系统获得多滚动混沌系统。并且通过在分形过程中改变复杂常数，获得具有不同形状的分形图，其也可用于在生成的多滚动膜混沌系统中产生不同的混沌吸引子。与其他多滚动混沌吸引子相比，所提出的多滚动混沌吸引子更容易调整滚动的数量。从仿真图可以看出，随着滚动的数量增加，系统相位图的大小变得越来越小。结果表明，新系统具有大量动态特性。

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