Synchronization dynamics of Colpitts circuits under resistive couplings reproduced by energy constraint

Synchronizations, one of collective behaviors, has been found in various interesting systems such as electronic devices and neuron-inspired circuits. The dynamical mechanism of nonlinear circuits remains to be an attracting topic. This paper focuses on the synchronization dynamics of Colpitts circuits. The circuit regarded as a bi-membrane neuron can exhibit complex dynamical characteristics under different parameter settings by combining theoretical analysis and numerical simulation. Based on the Lyapunov stability theory, it is proved that the drive-response circuit can achieve global exponential synchronization under unidirectional resistive and inductive couplings. A Hamilton energy function of the Colpitts circuit is deduced by employing the Helmholtz's theorem. The drive-response circuit with energy constraint is also able to show the synchronization. Finally, the synchronization mechanism of Colpitts circuit networks is investigated. It is found that the resistive coupling or the energy constraint has ability to promote the synchronization of the network. Compared to previous studies on Colpitts circuits with resistive or inductive couplings, our work uniquely integrates energy constraint to reveal a dual synchronization mechanism. This approach not only addresses the gap in understanding energy-driven synchronization in nonlinear circuits but also provides a novel framework for energy-efficient electronic system design. This study not only enriches the theoretical basis in the synchronization of nonlinear dynamics, but also provides important guidance for the design and optimization of corresponding electronic systems.