Dynamical and collective behaviors of enhanced photosensitive neuron model with memristor

A recently proposed biological neuron model, known as the photosensitive neuron model, has been introduced to estimate neuronal responses to external optical signals. This paper extends the model by incorporating a memristor to account for electromagnetic induction effects, thereby introducing memory-dependent dynamics and enriching the model's capacity to simulate biologically relevant phenomena such as bistability and chaos. The dynamical responses of the improved model are systematically analyzed, revealing that magnetic induction strength significantly influences firing behaviors, with chaotic regions diminishing as the strength increases. Importantly, the model exhibits bistability for specific magnetic induction strengths, characterized by the coexistence of periodic and chaotic attractors, providing a mechanism to model distinct neural states. Furthermore, a small-world network of the improved neurons is constructed, and its collective behaviors are investigated under varying parameters. By calculating the global order parameter, the network is shown to exhibit diverse synchronization patterns, including cluster synchronization and solitary states, demonstrating the enhanced ability of the model to capture complex collective dynamics.