<p>Neuromorphic circuits, inspired by biological neurons and synapses, can mimic complex firing modes and collective behaviors. Here, we construct a new neuron-inspired circuit connected by a vanadium dioxide (VO₂) memristor, a capacitor, and a Josephson junction in parallel. It is then shown that the equivalent circuit model can replicate neuron-like bursting behaviors. The generation mechanism behind bursting modes is uncovered using the fast-slow decomposition approach. Furthermore, we investigate the phase synchronization of two neuron-like models coupled via electrical synapses. This synchronization is demonstrated through both numerical simulations and theoretical analysis. Finally, the stability of a cellular neural network composed of neuron-like circuits is verified by Lyapunov stability theory. Interestingly, it is observed that the cellular neural network can exhibit abundant collective behaviors.</p>