Abstract:Chaos phenomenon is a unique behavior of nonlinear dynamical systems ubiquitous in nature, which is unpredictable and sensitive to initial conditions. Chaos synchronization is widely used in biology, medicine, secure communication and so on. In this paper, a four-dimensional dynamic system is established by parallel Josephson junction on the basis of Chua’s circuit, and its dynamic behavior is analyzed. The results show that the circuit can exhibit periodic and chaotic states. Secondly, combined with numerical simulation, we classify and discuss the complete synchronization behavior of capacitor coupling two periodic systems, two chaotic systems or periodic and chaotic system. The results show that the complete synchronization can be achieved by changing the coupling strength of two completely identical periodic systems or two completely identical chaotic systems, regardless of whether there is an external magnetic field. However, the coupling system with two different parameters cannot achieve perfect synchronization, but under the appropriate external magnetic field, almost complete synchronization can be achieved.