Symmetrically scaled coexisting behaviors in two types of simple jerk circuits
Abstract
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.
Keywords
Acknowledgements
This research issue was supported by grants from the National Natural Science Foundations of China under Grant Nos. 51777016 and 61801054.
Declaration of Competing Interest: The authors declare that they have no conflicts of interest. These authors contribute equally to this work.
Citation
Hua, M., Yang, S., Xu, Q., Chen, M., Wu, H. and Bao, B. (2020), "Symmetrically scaled coexisting behaviors in two types of simple jerk circuits", Circuit World, Vol. 47 No. 1, pp. 61-70. https://doi.org/10.1108/CW-02-2020-0028
Publisher
:Emerald Publishing Limited
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