Bursting synchronization and excitability of the bi-membrane neuron-like circuit under electromagnetic stimuli

Neuronal circuits involving two capacitors have an essential role in exploring biophysical mechanisms and mimicking brain-inspired devices. Given the dual-capacitor effect in nerve cells, we systematically investigate dynamical characteristics of the bi-membrane neuron-like (BMN) circuit subjected to a constant current source and alternating magnetic stimulus based on a magnetoelectric nonlinear metamaterial (MNM). Different from traditional single-membrane designs, the BMN circuit has a variety of rich structure, supporting more complex biological dynamics for enhanced neuromorphic computation. Through theoretical analysis and numerical simulation, it is found that the BMN circuit with an increased constant current exhibits neuronal excitability associated with a Hopf bifurcation. Based on Helmholtz's law, the energy function of the BMN circuit system is verified. Under the alternating magnetic stimulus, the BMN circuit can reproduce a chaotic bursting pattern by using numerical simulation. Finally, a BMN circuit network model with constant current source and alternating magnetic stimulus is constructed under resistive coupling. Using a master stability function (MSF) method, it is demonstrated that the BMN circuit network with chaotic and chaotic bursting patterns can achieve stable synchronization under suitable coupling parameters, and the regulation mechanism of coupling strength is elucidated. This study enriches the dynamic theory of the BMN circuit, providing a theoretical reference and practical guidance for network synchronization control and neuromorphic device design.