Continuously Bursting Simulations and Analytical Solutions of the Neocortical Neurons Model

Abstract

The well-known Hodgkin Huxley (HH) model employs the electrical circuit theory to describe the membrane potential of a cell in a giant squid axon. Hugh R. Wilson introduced human and mammalian neocortical neurons (HMNN) model which limits the potential nonlinearities to cubic polynomials while retains the same basic biophysics. This model has been used in neural dynamics, neural network, neural field theory, and epilepsy. Although mathematical methods have been applied to solve the HH model, a survey of recent papers reveals that HMNN model has not been solved analytically by the similar methods. In this work, a step homotopy analysis method (SHAM), an extended approach of the homotopy analysis method (HAM), is applied to solve HMNN model analytically for the first time. We present that the SHAM is an efficient method which yields high accuracy. The presented method is suitable for solving a variety of nonlinear dynamical systems.