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Self-organizations with fast-slow time scale in a memristor-based Shinriki’s circuit
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-10-10 , DOI: 10.1016/j.cnsns.2020.105569
Xiao-Bo Rao , Xu-Ping Zhao , Jian-She Gao , Jian-Gang Zhang

The structure of complex oscillations with two time scales generated by a novel memristor-based Shinriki’s circuit is studied in detail. Employing the stability phase diagrams, we identify the parameter regions of mixed-mode oscillations (MMOs) produced by each state variable, and classify the fast and slow properties of state variables according to the characteristics of these MMOs. Additionally, we exhibit the self-organizations of phases and describe how they are interconnected and how their complexity unfolds with control parameters varying. For several parameter combinations, in addition to recently reported shrimp-shaped cascades and “eye” of chaos, two kinds of interesting self-organizations, the shrimp cascade covered by four distinct numbers of peaks and “eye” of anti-chaos, are also discovered. A significant feature of these structures indicates that the fast-slow dynamics of the system depend not only on the state variables but also strongly on the parameter interval. The results of theoretical analyses obtained are verified by the Multisim simulation experiments. This paper will contribute to understanding the profound dynamical behaviors of the memristor-based circuit and open the possibility of studying hitherto unobserved phenomena.



中文翻译:

基于忆阻器的Shinriki电路中具有快速时标的自组织

详细研究了基于新型忆阻器的Shinriki电路产生的具有两个时标的复数振荡的结构。利用稳定相图,我们确定每个状态变量产生的混合模式振荡(MMO)的参数区域,并根据这些MMO的特性对状态变量的快速和慢速属性进行分类。此外,我们展示了阶段的自组织,并描述了它们如何相互连接以及随着控制参数的变化其复杂性如何发展。对于几个参数组合,除了最近报告的虾形串级和混沌的“眼”外,还有两种有趣的自组织,即由四个不同数量的峰覆盖的虾级联和反混沌的“眼”。发现。这些结构的显着特征表明,系统的快速慢速动力学不仅取决于状态变量,而且很大程度上取决于参数间隔。通过Multisim仿真实验验证了理论分析的结果。本文将有助于理解基于忆阻器的电路的深刻动力学行为,并为研究迄今未发现的现象提供了可能性。

更新日期:2020-10-30
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