Computational investigations of a model of neocortical electrorhythmogenesis

This thesis explores the dynamics of a physiologically realistic mathematical model of a neural population, whose experimental analogue is the electroencephalogram. This spatially homogeneous model consists of two neural populations, one excitatory and one inhibitory, coupled together via synaptic dynamics. Detailed computational investigations of this model shows that it is capable of supporting physiologically plausible limit cycle and point attractor dynamics under a wide variety of parameterisations. Investigations also showed that for certain parameterisations the mathematical model exhibits chaotic dynamics and generalised multistability. Lyapunov exponents were determined using an implementation of the Christiansen-Rugh algorithm. Chaos in the model was found to exhibit special structure in parameter space called fat fractal scaling. Generalised multistability with two or three coexisting attractors was found to exist in the model, which included coexisting chaos and limit cycle activity. These findings have two implications: firstly, the prediction of chaos coupled with the noisy environment of real brains may lead to the generation of a dynamical melange which complicates the search for chaos in the electroencephalogram; and secondly, the presence of coexisting chaotic and limit cycle dynamics gives some support to Freeman's idea that perception represents a metastable dynamical phenomenon.