Identification of a free energy functional in an integro-differential equation model for neuronal network activity Original Research Article

Neuronal activity in a synaptically-coupled network of excitatory and inhibitory neurons can be modeled by an integro-differential equation. Solutions to this equation represent cellular activity and are dependent on the neuronʹs spatial location and time. One area of interest to researchers has been the identification and analysis of stationary bump solutions which are steady states of the evolution problem. In this brief report, we furnish an energy functional. It is expected that this energy will be useful in analyzing the dynamic behavior of the system, finding steady states, studying the stability of these stationary solutions, and developing numerical methods.