Symmetrically scaled coexisting behaviors in two types of simple jerk circuits

Hua Mengjie; Yang Shuo; Xu Quan; Chen Mo; Wu Huagan; Bao Bocheng

摘要

PurposeThe purpose of this paper is to develop two types of simple jerk circuits and to carry out their dynamical analyses using a unified mathematical model.Design/methodology/approachTwo types of simple jerk circuits only involve a nonlinear resistive feedback channel composited by a nonlinear device and an inverter. The nonlinear device is implemented through parallelly connecting two diode-switch-based series branches. According to the classifications of switch states and circuit types, a unified mathematical model is established for these two types of simple jerk circuits, and the origin symmetry and scale proportionality along with the origin equilibrium stability are thereby discussed. The coexisting bifurcation behaviors in the two types of simple jerk systems are revealed by bifurcation plots, and the origin symmetry and scale proportionality are effectively demonstrated by phase plots and attraction basins. Moreover, hardware experimental measurements are performed, from which the captured results well validate the numerical simulations.FindingsTwo types of simple jerk circuits are unified through parallelly connecting two diode-switch-based series branches and a unified mathematical model with six kinds of nonlinearities is established. Especially, the origin symmetry and scale proportionality for the two types of simple jerk systems are discussed quantitatively. These jerk circuits are all simple and inexpensive, easy to be physically implemented, which are helpful to explore chaos-based engineering applications.Originality/valueUnlike previous works, the significant values are that through unifying these two types of simple jerk systems, a unified mathematical model with six kinds of nonlinearities is established, upon which symmetrically scaled coexisting behaviors are numerically disclosed and experimentally demonstrated.

机译：本文的目的目的是开发两种类型的简单的JERK电路，并使用统一的数学模型进行动态分析.Design/Methodology/AppropTWO类型的简单Jerk电路仅涉及由非线性设备构成的非线性电阻反馈通道和逆变器。非线性装置通过并行连接两个基于二极管切换的系列分支来实现。根据开关状态和电路类型的分类，为这两种类型的简单JERK电路建立了统一的数学模型，由此讨论了原点对称性和比例与原点平衡稳定性。两种类型的简单混凝土系统中的共存分岔行为被分叉图揭示，并且通过相块和吸引力盆地有效地证明了原点对称性和比例比例。此外，执行硬件实验测量，从中捕获的结果良好地验证了数值模拟。通过并行连接基于二极管交换的系列分支和具有六种非线性的统一数学模型来统一简单的JERK电路的FindingStwo类型。。特别地，定量讨论了这两种简单的JERK系统的原点对称性和比例比例。这些JERK电路都是简单且廉价的，易于物理实施，这有助于探索基于混乱的工程应用程序。以前/ ValueUnlike以前的作品，通过统一这两种类型的简单Jerk系统，一个统一的数学建立了具有六种非线性的模型，对称缩放的共存行为是数值披露和实验证明的。

Symmetrically scaled coexisting behaviors in two types of simple jerk circuits

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