BIS Processes in the Human Neural Networks and Asymptotic Periodic Solutions of the Evolution Equations in the Brain Nanosystem using Jacobi Elliptic Function

Abstract

Our perseverance is dependent upon the normal functioning and fluctuation of the brain. That functioning involves complex electrical activities. These in turn generate subtle waves which were first noticed and studied by Hans Berger. These are essentially electrical rhythms in the brain which, when recorded by means of instruments called electroencephalograms or EEG on a roll of paper, appear as complex wave forms. In this paper, based on Jacobi elliptic function expansion method, the Lame equation, and the Lame functions, the stationary periodic solutions to some non linear evolution equations for the brain nanosystem have been derived. At the same time the perturbation method is applied to obtain their asymptotic series solutions. We have tried our best here to find out all the possible solutions of the equations evolved due to perturbation in the brain nanosystem hence distracting the total human networks.

Keywords: Human neural networks, brain nanosystem, Lame equation, BIS (Breakdown of Integrated System), Jacobi elliptic function