Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits

Yu-meng XU; Zhao YAO; Aatef HOBINY; Jun MA

doi:10.1631/FITEE.1800499

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Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits

Regular Papers | Updated：2022-05-19

- Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits
- 基于混沌电路电容器连接的微分耦合同步
- Frontiers of Information Technology & Electronic Engineering Vol. 20, Issue 4, Pages: 571-583(2019)
- Affiliations：
  
  Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
  NAAM-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
- Author bio：
  
  Jun MA, E-mail: hyperchaos@163.com
- Funds：
- DOI：10.1631/FITEE.1800499
  CLC： O59;TN710
- Received：21 August 2018，
  
  Revised：2019-;1-14，
  
  Published Online：23 January 2019，
  
  Published：2019-04
- Accepted：
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Yu-meng XU, Zhao YAO, Aatef HOBINY, et al. Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(4): 571-583.
DOI：

Yu-meng XU, Zhao YAO, Aatef HOBINY, et al. Differential coupling contributes to synchronization via a capacitor connection between chaotic circuits[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(4): 571-583. DOI： 10.1631/FITEE.1800499.

摘要

非线性振子和电路常用于研究耦合同步和一致性问题。完全同步是指所有振子保持相同幅度和相位，主要发生在完全相同振子之间。相位同步是指振子保持步调节律同步而幅度不同。对于无维动力学系统和振子，同步依赖于耦合变量的选择和耦合方式。非线性电路中电阻常用于连接两个或以上电路，触发电压耦合可对耦合电路反馈调制。本文采用电容器耦合两个Pikovsk-Rabinovich (PR)电路，这种电场耦合机制为微分耦合提供了依据。讨论了对称性和错位耦合下两个混沌电路的同步稳定性问题。在电阻耦合下，两个混沌电路容易完全同步。进一步讨论电容器耦合，发现当耦合电容器选择合适电容值时，两个耦合电路同步可被有效控制，且耦合电容器能量流有助于对同步的调控。混沌电路的同步实现和耦合通道有关，如对称性耦合容易完全同步，错位耦合有利于相位同步。电容器对应电场耦合能降低耦合器件能量（焦耳热）消耗，加强两个耦合电路能量输运和交换，从而实现混沌电路同步。

Abstract

Nonlinear oscillators and circuits can be coupled to reach synchronization and consensus. The occurrence of complete synchronization means that all oscillators can maintain the same amplitude and phase

and it is often detected between identical oscillators. However

phase synchronization means that the coupled oscillators just keep pace in oscillation even though the amplitude of each node could be different. For dimensionless dynamical systems and oscillators

the synchronization approach depends a great deal on the selection of coupling variable and type. For nonlinear circuits

a resistor is often used to bridge the connection between two or more circuits

so voltage coupling can be activated to generate feedback on the coupled circuits. In this paper

capacitor coupling is applied between two Pikovsk-Rabinovich (PR) circuits

and electric field coupling explains the potential mechanism for differential coupling. Then symmetric coupling and cross coupling are activated to detect synchronization stability

separately. It is found that resistor-based voltage coupling via a single variable can stabilize the synchronization

and the energy flow of the controller is decreased when synchronization is realized. Furthermore

by applying appropriate intensity for the coupling capacitor

synchronization is also reached and the energy flow across the coupling capacitor is helpful in regulating the dynamical behaviors of coupled circuits

which are supported by a continuous energy exchange between capacitors and the inductor. It is also confirmed that the realization of synchronization is dependent on the selection of a coupling channel. The approach and stability of complete synchronization depend on symmetric coupling

which is activated between the same variables. Cross coupling between different variables just triggers phase synchronization. The capacitor coupling can avoid energy consumption for the case with resistor coupling

and it can also enhance the energy exchange between two coupled circuits.

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references

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