The Dynamics of a Glia-Modulated Neural Network and its Relation to Brain Functions

Abstract

The complex patterns of electroencephalograms(EEGs) have made it very difficult for physiologists and pathologists to interpret the relationships to brain functions. A possible way to approach this problem is to study the dynamic behaviors of a mathematical model of large scale neuron network based on the fundamental electrical properties of neurons and their interrelationships, as done by J.D. Cowan and his co-workers (Cowan 1974; Ermentrout and Cowan 1979, 1980). They proposed two coupled non-linear integro-differential equations, comprising two types of neurons (excitatory and inhibitory), and analysed them by bifurcation theory. Because of the statistical nature of their treatment, all complexities of neurobiological details, such as the plasticities of neurons and synapses, may be taken into consideration, but their results still are very difficult to compare with real EEG patterns, especially those of conscious human beings, which display highly irregular, quasi-random forms. These kinds of behaviors may also be found in general dynamic systems and are called chaotic. This paper is an investigation of the problems concerning the relations between chaotic behaviors of neural network dynamics and EEG patterns, i.e., brain functions.