Abstract:
The aim of this thesis is to deluge the latest studies in chaotic dynamics and their
relevance in neural computing, as also to inspect a new learning algorithm for a network
of chaotic spiking neurons as it is recently proposed by Nigel Crook et al. [1]. The thesis
will tackle the latest research in the field of information processing and chaotic neural
networks, and will contribute to the recent work of Nigel Crook et al. [1] by finding a
suitable learning algorithm for chaotic neurons. The learning algorithm based on
biological realism will be implemented in a network of chaotic spiking neurons and
evaluated accordingly.
After the extensive scientific studies in neuroscience during the last decade, which have
been supported with experimental evidence, much explanation of the internal brain
processes that lead the brain to learn and exhibit ‘intelligent behavior’ has been revealed.
Such new ‘explanation’ relies on chaotic neurodynamics and is originally based on the
experiments of Freeman and Skarda [2, 3]. The experiments show chaotic activity in the
olfactory bulb of a rabbit’s brain when the rabbit is in a ‘perceptual’ state [2, 3]. Such
studies led to the hypothesis, given by Freeman, “The physiology of perception” in 1991,
which claims that “Chaos may be the chief property that makes the brain different from
an artificial-intelligent machine” [3]. Walter J. Freeman is considered as being the
‘father’ of chaotic neurodynamics, his hypothesis gained major attention in the scientific
community and led to further scientific results [7, 39, 40, 41].
Last but not least, we conclude that emulating chaotic neuro dynamics is a fundamental
strategy in the design of new models of artificial neural networks. We’ll point out on the
necessary links between neural computing and cognitive computations, nonlinear
dynamics and chaotic neuro dynamics. This research is an extension to a wider research
concerned in improving the capabilities of artificial neural networks by the exploit of non
linear dynamical systems [1]. The thesis will go in depth in presenting the topic, will
contribute to the latest research of applying chaotic dynamics in neural information
processing and specifically to the work of N. Crook [1]. The fundamental theories behind
the Nonlinear Dynamic State - NDS - Neuron invention [1], as also its roots which are
found in Pyraguas theory of chaos control [5, 26] and its insights in Freeman theories on
chaotic neuro dynamics and strange attractors are presented. The main idea in the NDS
neuron research relies in stabilizing Unstable Periodic Orbits called UPOs of strange
attractors to model neural states with these UPOs. If this is the case then the NDS neuron
would have an unlimited number of states it could synchronize onto, since the number of
possible UPOs is theoretically infinite [1].
My contribution went through the analysis of NDS neurons dynamics and their behavior
with time when they are recurrently connected. The analysis, research and development
resulted in the revelation of an expedient biological phenomenon which suits the
dynamics of these neurons and learning capabilities, while ensuring their states
adaptation, stability and synchronization.
Description:
M.S. -- Faculty of Natural and Applied Sciences, Department of Computer Science, Notre Dame University, Louaize, 2007; "A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Science"; Includes bibliographical references (leaves 52-55).