Firing patterns, attractor regulation and energy analysis of coupled FitzHugh-Nagumo neural networks

Bridging artificial intelligence and the human brain is crucial for overcoming current technological limitations, and full neuronal synchronization can play a central role in cerebral information encoding and transmission. In this article, we will investigate the dynamical behaviors of a homogeneous network of FitzHugh–Nagumo neuron pairs coupled with electrical synapses through the discrete implicit mapping method. We then characterize representative firing patterns and trace the evolution of periodic discharge modes by constructing bifurcation trees as the coupling strength varies. Furthermore, by leveraging the structural similarity of the coupled system, we achieve three-dimensional control of attractor bias and amplitude. Using the normalized average synchronization error as a quantitative metric, we identify the principal internal and external factors that govern synchronization in homogeneous electrically coupled neuronal networks. In addition, we examine energy variations associated with system control by linking attractor control strategies to synchronous firing behaviors. Collectively, these findings provide theoretical and methodological support for the study of neural synchronization, and they may also inform the development of intervention strategies for neurological disorders and contribute to broader advances in neuroscience.