Purpose

The 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/approach

Two 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.

Findings

Two 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/value

Unlike 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.

中文翻译：

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两种简单的急动回路中的对称尺度共存行为

目的

本文的目的是开发两种简单的急动回路，并使用统一的数学模型进行动力分析。

设计/方法/方法

两种简单的急动电路仅涉及由非线性器件和逆变器合成的非线性电阻反馈通道。通过并联连接两个基于二极管开关的串联支路来实现非线性器件。根据开关状态和电路类型的分类，为这两种简单的急动电路建立了统一的数学模型，并讨论了原点对称性和比例比例以及原点平衡稳定性。通过分叉图揭示了两种类型的简单混蛋系统中共存的分叉行为，并且通过相图和吸引盆有效地证明了原点对称性和比例比例。此外，还进行了硬件实验测量，

发现

通过并联连接两个基于二极管开关的串联支路，将两种简单的急动电路统一起来，并建立了具有六种非线性的统一数学模型。特别是，定量讨论了两种类型的简单混蛋系统的原点对称性和比例比例。这些急动回路都很简单，便宜，易于物理实现，有助于探索基于混沌的工程应用。

创意/价值

与以前的工作不同，重要的价值在于通过将这两种类型的简单混蛋系统统一起来，建立了具有六种非线性的统一数学模型，并在此数学模型上公开了对称缩放的并存行为并进行了实验证明。