Model neurons that incorporate aspects of complex dynamics observed either in the isolated biological neuron or in assemblies of several biological neurons. Some of the models with complex dynamics, mentioned in the main text of this article, are the Aihara’s model neuron, the Bifurcation Neuron proposed by Nabil Farhat, RPEs networks, Kaneko’s CMLs, and Walter Freeman’s K Sets.
Published in Chapter:
Chaotic Neural Networks
Emilio Del-Moral-Hernandez (University of São Paulo, Brazil)
Copyright: © 2009
|Pages: 7
DOI: 10.4018/978-1-59904-849-9.ch043
Abstract
Artificial Neural Networks have proven, along the last four decades, to be an important tool for modelling of the functional structures of the nervous system, as well as for the modelling of non-linear and adaptive systems in general, both biological and non biological (Haykin, 1999). They also became a powerful biologically inspired general computing framework, particularly important for solving non-linear problems with reduced formalization and structure. At the same time, methods from the area of complex systems and non-linear dynamics have shown to be useful in the understanding of phenomena in brain activity and nervous system activity in general (Freeman, 1992; Kelso, 1995). Joining these two areas, the development of artificial neural networks employing rich dynamics is a growing subject in both arenas, theory and practice. In particular, model neurons with rich bifurcation and chaotic dynamics have been developed in recent decades, for the modelling of complex phenomena in biology as well as for the application in neuro-like computing. Some models that deserve attention in this context are those developed by Kazuyuki Aihara (1990), Nagumo and Sato (1972), Walter Freeman (1992), K. Kaneko (2001), and Nabil Farhat (1994), among others. The following topics develop the subject of Chaotic Neural Networks, presenting several of the important models of this class and briefly discussing associated tools of analysis and typical target applications.