Overview
- Recent studies of bifurcations have inspired a new approach to brain modelling * Shows how some synaptic organisations have especially rich dynamic behaviour *
- Hoppensteadt is a well-known author
Part of the book series: Applied Mathematical Sciences (AMS, volume 126)
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Table of contents (13 chapters)
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Front Matter
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Introduction
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Front Matter
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Derivation of Canonical Models
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Front Matter
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Analysis of Canonical Models
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews:
"...After the introduction, written according to the authors in ordinary language, and well readable even for laymen, follows a nicely written Chapter 2 on bifurcations in neuron dynamics which must be read. Here also spiking and bursting phenomena are clearly described. Chapter 3 contains a short sketch of nonhyperbolic (when the Jacobian matrix of (1) has at least one eigenvalue with zero real part) neural networks. The remaining part of the book is mainly devoted to canonical models (Chapter 4), their derivation (Chapters 6--9), and their analysis (Chapters 10--12). The term canonical model is not precisely defined here. The authors say that a model is canonical if there is a continuous change of variables that transforms any other model from a given class into this one. As the method of deriving the canonical models, the authors exploit the normal form theory. Canonical models treated in the book have only restricted value: They provide information about local behavior of (1) when there is an exponentially stable limit cycle but they say nothing about global behavior of (1), including the transients. The last Chapter 13 describes the relationship between synaptic organizations and dynamical properties of networks of neural oscillators. In other words, the problem of learning and memorization of phase information in the weakly connected network of oscillators corresponding to multiple Andronov-Hopf bifurcation is treated analytically.
Surprisingly the book ends without any conclusions. Also there are no appendices to the book. The references are representative and sufficiently cover the problematics treated in the book." (Ladislav Andrey, Mathematical Reviews)
Authors and Affiliations
Bibliographic Information
Book Title: Weakly Connected Neural Networks
Authors: Frank C. Hoppensteadt, Eugene M. Izhikevich
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-1-4612-1828-9
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1997
Hardcover ISBN: 978-0-387-94948-2Published: 10 July 1997
Softcover ISBN: 978-1-4612-7302-8Published: 30 September 2012
eBook ISBN: 978-1-4612-1828-9Published: 06 December 2012
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: XVI, 402
Topics: Analysis, Mathematical and Computational Biology, Neurosciences