ЭФФЕКТЫ ДИСКРЕТИЗАЦИИ ПРИ ЧИСЛЕННОМ ИССЛЕДОВАНИИ МОДЕЛИ НЕЙРОНА ХОДЖКИНА - ХАКСЛИ

Abstract

Computer design is a valuable tool in the course of designing neuro-morphic systems. In particular it allows investigating basic mechanisms of neuron pulse activities in networks. For computer modeling it is necessary to digitize a continuous model of the system by means of the application of discrete operators able to keep basic properties of a prototype. But the accuracy of discrete models may decrease because of negative effects caused by the type of the method used, by a discretization pitch and errors in rounding off. 
 This fact is significant for the analysis of non-linear systems to which belong the models of biological neurons. As a possible solution of the problem may be the development of specialized tools for the analysis of dynamic systems with the focus upon numerical methods used. In this paper by the example of the modeling of the neuron described by Hodgkin-Huxley classical equations there is considered a set of widespread methods for ODU solution. In the course of investigations there are shown possible negative consequences of incorrect use of some discrete operators. In the paper the results of two sets of computer experiments are presented. The first ones determine the limitations for the practical use of the methods of the first accuracy order during modeling neurons in the mode of resonance generation of action potentials. The second ones show discretization effects connected with chaotic modes of neurons functioning: incorrect behavior of discrete models which is manifested in the emergence of chaotic transition processes. The investigation results may be used at the formation of modeling tool packages both, non-linear dynamic systems in the whole, and neuro-morphic systems in particular.