Dynamic Behavior of Coupled Neuron System from a Game-Theoretic Standpoint

This paper is concerned with the theoretical investigation of game theory concepts in analyzing the behavior of dynamically coupled oscillators. Here, we claim that the coupling strength in any neuronal oscillators can be modeled as a game. We formulate the game to describe the effect of pure-strategy Nash equilibrium on two neuron systems of Hopf-oscillator and later demonstrate the application of the same assumptions and methods to N x N neuronal sheet. We also demonstrate the effect of the proposed method on MNIST data to show the equilibrium behavior of neurons in a N x N neuronal grid for all different digits. A significant outcome of the paper is a modified Hebbian algorithm, which adapts the coupling weights to neural potential resulting in a stable phase difference. Which in turn, makes it possible for an individual neuron to encode input information.