Learning and memory in chaotic spiking neural models

The broad aim of this research is to explore the possibilities of using the properties that chaos provides to carry out information processing tasks. This has been done in the context of chaotic spiking neural networks (CSNNs). Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Biological research suggests that chaos plays an important role in carrying out information processing tasks in human brains. Also, great interest has been given recently to spiking neural networks (SNNs). Moreover, research in the field of SNNs has found recently that such networks have maximum performance at the ‘edge of chaos‘. All of the previous motivations suggest that CSNNs will have better performance than other types of models. The specific aims of this research are to investigate the dynamics of a chaotic spiking neuron model, the nonlinear dynamic state neuron (NDS), and study networks of such neurons in terms of stability and learning algorithms. The investigation of this model has been carried out experimentally and analytically. The experimental approach has partially explained some quantitative and qualitative properties of the NDS model such as the control mechanism, the reset mechanism, and the way the model exhibits dynamic behaviours in phase space. This thesis also presents a detailed mathematical analysis of the NDS model which provides a deeper understanding of these and other properties of the model. This analysis has revealed how the control mechanism works, the role of the reset mechanism, the dynamic behaviours the NDS model can exhibit in phase space, and has implied that the NDS model is chaotic. Networks of NDS neurons have also been studied in terms of stability. Furthermore, different learning algorithms have been proposed and investigated. It is shown experimentally in this thesis that both the reset mechanism and the self-feed back control mechanism are important for the NDS model to work and to stabilise to one of the large number of available unstable periodic orbits (UPOs) in its attractor. The mathematical analysis of the dynamics of single NDS neuron has shown major analytical differences compared with the Réssler system. In networks of NDS neurons, an energy function has been formulated to study the stability in such networks. Compared with traditional Hopfield nets, networks of NDS neurons show better stability. Two learning algorithms have been devised to investigate the possible exploitation of the rich dynamic behaviours that are available in the NDS attractor. Both the experimental and analytical investigations strongly suggests how the internal dynamics of NDS neurons provides a rich set of dynamic behaviours that are easy to control and stabilise. This wide range of dynamic behaviours are maximized in networks of NDS neurons with specific settings and can be exploited to carry out information processing tasks. This can be achieved through the proposed adaptation algorithms. Given a suitable learning algorithm, the dynamics of small networks of NDS neurons can be used to learn a sequence of input patterns that may represent a movement for example. Methods of learning would be based on different elements such as synchronization among the NDS neurons, self-feedback control, pace maker and self-organizing.

Grantor dc:publisher

Oxford Brookes University

Author dc:creator

• Alhawarat, Mohammad Omar Ibrahim

Contributors dc:contributor

• Crook, Nigel
• Olde Scheper, Tjeerd

Statement dc:rights

• All rights reserved

Language dc:language

en

DOI dc:identifier

https://doi.org/10.24384/7eq2-gg95

OAI identifier oai:identifier

tle:64950227-2cbb-4353-b51d-a40d1de7ea6b:d6bd9758-527a-46cd-bfe2-c433766e8fca:1