Chaotic systems for pattern recognition and brain modelling

Abstract

The main aim of this thesis and our research endeavor is to propose methods and algorithms for controlling models related to the brain, in order, for them to recognize and to modify their levels of chaos. We investigated five problems: (1) We presented all original and novel strategy for Pattern Recognition (PR) using Chaotic Neural Networks. The algorithm is based on a formal hypothesis proposed by Freeman [56], who developed a model for an olfactory system. He conjectured that the brain is essentially a chaotic system in the absence of a stimulus (pattern) that it is supposed to recognize. During perception, when the attention is focussed on any sensory stimuli, the brain activity become periodic. We have designed a PR system, namely a Chaotic Neural Network, which demonstrates such a phenomenon. (2) We proposed a new approach for modelling a PR system which loses its ability to recognize, even though the quality of the stimulus is perfect. By using a Chaotic Neural Network, we have provided a chaotic rationale for both perception and the lack thereof, even in cases when the stimulus is error-free. (3) We investigated in the piriform cortex (modelled as a large scale network), the dependence of the level of chaos as a function of a few variables (or parameters). Our aim was to discover methods by which we could increase the level of chaos in almost synchronized large scale networks, as in the epileptic brain. (4) We studied a classical model of the Hodgkin-Huxley (HH) neuron, and analytically proved its stability properties and the existence of a brief current pulse, which, when delivered to the HH neuron during its repetitively firing state, annihilates its spikes. The experimental properties of this phenomenon have also been investigated. (5) We presented a stability analysis for small scale networks consisting of Bursting neurons. We proved that if the coupling between the neurons is arbitrarily small, the network exhibits chaos and that the network rapidly converges to a synchronized behavior, implying that increasing the number of neurons does not contribute significantly to the synchronization of the individual bursting neurons. The consequences of this behavioral synchronization, and its implications to a new hypothesis for the genesis of epileptic seizures have also been analyzed. Finally, we have developed methods for controlling the behavioral synchronization of the network. The thesis also lists various open problems and avenues for future research.