Research on synchronization in a Josephson junction-memristor system with dual capacitive membranes

Neuronal synchronization plays a pivotal role in brain function, yet conventional neuron models often overlook crucial membrane properties when considering synchronization. There is a need for a comprehensive exploration of the effects of Josephson junctions (JJ) and memristors in nonlinear circuits, particularly in elucidating synchronization states, to better understand this aspect of neuronal behavior. This research employs a dual-capacitance neuron model, integrating memristors and JJ, to investigate their collective influence in coupled systems. By adjusting the gain ratio of coupling strength, introducing noise, and modulating external stimuli, a detailed investigation into neuronal dynamic behaviors and synchronization patterns is undertaken. The findings illustrate that neuronal synchronization is intricately influenced by the ratio of coupling strength, noise levels, and external stimuli. Optimal synchronization occurs with moderate stimuli and coupling gain ratios, while excessive levels inhibit synchronization, resulting in delayed synchronization onset. Moreover, the study demonstrates the system's robustness against Gaussian white noise models. These findings have broad implications, spanning from the diagnosis and treatment of neurological disorders to advancements in brain-machine interfaces and neural modulation therapies. Understanding neuronal synchronization not only enhances cognitive functions but also paves the way for innovative solutions in neurological interventions.