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Based on the principle of energy coding, an energy function of a variety of electric potentials of a neural population in cerebral cortex is formulated. The energy function is used to describe the energy evolution of the neuronal population with time and the coupled relationship between neurons at the subthreshold and the suprathreshold states. The Hamiltonian motinn equation with the membrane potential is obtained from the neuroelectrophysiological data contaminated by Gaussian white noise. The results of this research show that the mean membrane potential is the exact solution of the motion equation of the membrane potential developed in a previously published paper. It also shows that the Hamiltonian energy function derived in this brief is not only correct but also effective. Particularly, based on the principle of energy coding, an interesting finding is that in some subsets of neurons, firing action potentials at the suprathreshold and some others simultaneously perform activities at the subthreshold level in neural ensembles. Notably, this kind of coupling has not been found in other models of biological neural networks. Index Terms--Coupled neural population, energy coding, energy evolution, Hamiltonian function.

Studying neural coding through neural energy is a novel view. In this paper, based on previously proposed single neuron model, the correlation between the energy consumption and the parameters of the cortex networks (amount of neurons, coupling strength, and transform delay) under an oscillational condition were researched. We found that energy distribution varies orderly as these parameters change, and it is closely related to the synchronous oscillation of the neural network. Besides, we compared this method with traditional method of relative coefficient, which shows energy method works equal to or better than the traditional one. It is novel that the synchronous activity and neural network parameters could be researched by assessing energy distribution and consumption. Therefore, the conclusion of this paper will refine the framework of neural coding theory and contribute to our understanding of the coding mechanism of the cerebral cortex. It provides a strong theoretical foundation of a novel neural coding theory—energy coding. [ABSTRACT FROM AUTHOR]