Field coupling-induced synchronization via a capacitor and inductor

Abstract

Resistor-based voltage coupling is often used to realize complete synchronization between identical nonlinear circuits while phase synchronization is investigated between non-identical nonlinear circuits (periodic or chaotic oscillation). Indeed, the coupling resistor used to consume certain Joule heat and energy before reaching the synchronization target when continuous current passed across the coupling device. In this paper, capacitor and inductor is paralleled with one coupling resistor, respectively, and the coupling devices are used bridge connection between two LC hyperchaotic circuits for investigating synchronization problems. As a result, the coupling channel can be activated to propagate energy and balance the outputs voltage from the two circuits. The dimensionless dynamical equations are obtained by applying scale transformation on the circuit equations when field coupling is switched on. It is found that the threshold of coupling intensity for reaching synchronization and the power consumption of controller can be decreased when the coupling resistor is paralleled with on capacitor or inductor. The mechanism could be that involvement of coupling capacitor(or inductor) can trigger time-varying electric field (or magnetic field), and the energy flow of field coupling via coupling capacitor (or inductor) can contribute the exchange of energy in the coupled nonlinear circuits. It can give insights to investigate synchronization on chaotic systems, neural circuits and neural networks including synapse coupling and field coupling. Finally, the experimental results on circuits are also supplied for further verification.