Synchronization behavior of memristive FitzHugh-Nagumo neurons in time-varying networks under external stimuli

Synchronous firing of neurons is a key mechanism for ensuring coordination between neurons and effective integration of information. Neuronal networks change over time and are influenced by external stimuli, and exploring how these factors affect the synchronization capabilities of the network and their relationship with energy fluctuations is an important issue. This study investigates the synchronization and energy changes of a memristive FitzHugh-Nagumo neuronal network with time-varying topology under external stimuli. The results show that external stimuli affect the synchronization of the network. Larger coupling strength, along with appropriate amplitude and frequency, can effectively drive the network from an asynchronous to a synchronous state. Furthermore, as neurons tend to synchronize, their energy changes become increasingly consistent. The conditions for stable synchronization of the network are analyzed using the master stability function method, confirming the consistency between theoretical and numerical results and revealing the key role of rewiring probability in synchronization. The generality of the results is confirmed by varying network size and average degree. These findings indicate that external stimuli and time-varying topology play crucial roles in regulating collective behaviors in neuronal networks, providing new perspectives and theoretical support for the functional understanding and regulation of the nervous system.