Initial-condition-controlled synchronization behaviors in inductively coupled memristive Chua’s circuits

Field coupling via capacitor, inductor, or memristor has been applied for synchronization and consensus between nonlinear circuits and neural systems. The initial-condition-controlled synchronization behaviors therein are attractive to chaos-based applications and have not been intensively explored. In this paper, inductor coupling is applied between two memristive Chua’s circuits to investigate the synchronization behaviors controlled by the coupling inductor and the initial conditions of each coupled terminals. Based on the dimensionless model, the error functions and similarity indexes for memristive and non-memristive variables are calculated to evaluate the synchronicity of the inductively coupled system. The results show that complete, lag, and parallel-offset synchronization behaviors can be realized by selecting different inductance and initial condition values for the coupling inductor. Moreover, the synchronization behaviors can be flexibly tuned from two coupled terminals by adjusting their initial conditions. Experimental verifications are finally performed using FPGA-based digital platform. This synchronization scheme and feature may promote the implementations of chaos-based applications for multi-stable dynamical systems.