Energy Evolution of Neural Population under Coupling Condition

Abstract

On the based of principle of the energy coding, an energy function of variety of electric potential of neural population in cerebral cortex is proposed. The energy function is used to describe the energy evolution of neuronal population with time, and the coupled relationship between neurons at sub-threshold and at supra-threshold status. We obtain the Hamiltonian motion equation with the membrane potential under condition of Gaussian white noise according to neuro-electrophysiological data. The results of research show that the mean of the membrane potential obtained in this paper is just exact solution of motion equation of membrane potential in previous published paper. It is showed that the Hamiltonian energy function given in the paper is effective and correct. Particularly, by using the principle of energy coding we obtained an interesting result which is in subsets of neurons firing action potentials at supra-threshold and others simultaneously perform activities at sub-threshold level in neural ensembles. As yet, this kind of coupling in all models of biological neural network has not been presented.