Synchronization in FitzHugh-Nagumo Neuronal Networks

Abstract

Some of the most interesting neuroscience problems, fundamental to the field, are inherently mathematical. Central problems include understanding how cellular and network level mechanics of the peripheral and central nervous system coordinate to encode, process, and learn information, and how the Central Nervous System (CNS) is able to synchronize brain-wide neural activity. Answering these questions requires understanding how neuronal circuits react to stimuli and interact with one another to process information specific to their roles within a network. To simulate these intercellular dynamics, FitzHugh-Nagumo neurons were connected through incoming and outgoing voltage currents to form dynamic networks. External stimuli consisting of both excitatory and inhibitory signals were sent through the network. As the network’s connectivity coefficient increased, neurons began to synchronize. In some cases neuronal activity segregated and competed so that neither signal dominated the artificial network, underlining the importance of the relationship between signal and architecture in functional, biological circuits. Biological components which have been implicated in network synchronization, and how they could be mathematically implemented in future network simulations were discussed.