Synchronization realization between two nonlinear circuits via an induction coil coupling

  • Zhao Yao
  • Jun MaEmail author
  • Yuangen Yao
  • Chunni Wang
Original Paper


Nonlinear chaotic circuits can be mapped into dimensionless dynamical systems by applying scale transformation. For synchronization control, linear voltage coupling via resistor has confirmed its effectiveness by applying negative feedback on the coupled circuits and nonlinear systems. In fact, resistor-based voltage coupling just bridges the electric devices of nonlinear circuits by imposing appropriate feedback current. Indeed, inductor (or induction coil) can also connect the electric devices and input appropriate stimulus feedback as induced electromotive force, and thus the coupled circuits can be regulated. In this paper, two Chua circuits are coupled by an inductor, which connects one capacitor of the coupled Chua circuits, and magnetic field coupling is activated because time-varying magnetic field and induced electromotive force are generated in the coupling inductor. For numerical approach and dynamical analysis, scale transformation is applied to get dimensionless dynamical systems under magnetic field coupling. Then the controllable parameter mapped from the coupling inductor is adjusted carefully to detect the synchronization approach. The same investigation is also carried out on the circuit platform Multisim. It is found that inductor coupling can benefit the realization of synchronization between two chaotic Chua systems. Complete synchronization can be reached between two identical circuits when the inductor coupling is activated with appropriate intensity. While phase synchronization can be stabilized between two non-identical circuits, chaotic oscillation can be suppressed by periodic Chua circuit under inductor coupling. The potential mechanism for inductor-based synchronization can be explained as magnetic field coupling, which field energy can be propagated via the coupling inductor with time-varying induced electromotive force, and it can give possible insights to know the information encoding between neurons and neural circuits.


Field coupling Chua circuit Synchronization Inductor coupling Bifurcation 



This Project is supported by National Natural Science Foundation of China under Grants 11765011 and 11672122. The authors give thanks to Dr. F Q Wu for his helpful discussion and numerical checking.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no any conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhysicsLanzhou University of TechnologyLanzhouChina
  2. 2.School of ScienceChongqing University of Posts and TelecommunicationsChongqingChina
  3. 3.Department of Physics, College of ScienceHuazhong Agricultural UniversityWuhanChina

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