  Synchronous control of nonlinear circuits is of great importance in many
fields. In this paper, a capacitor is used for closed-loop coupling of three
dual-vortex attractor Chua circuits with the same circuit parameters and
different initial conditions, and the corresponding synchronization processes
and synchronization effects are investigated. It is found that, for the
capacitor, the closed-loop coupling can completely synchronize the three Chua
circuits. And there exists a critical coupling strength $\delta_{critical}^C$
that can be calculated, and when the coupling strength is between the critical
coupling strength $\delta_{critical}^C$ and the upper coupling strength
$\delta_{max}^C$, the three circuits can be completely synchronized very
quickly. Moreover, the results show that the unidirectional coupling cannot
make the circuit system completely synchronized. Finally, we also verify the
correctness of the calculation by circuit simulation experiments.
