Weakly Connected Neural Networks
(Sprache: Englisch)
Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both...
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Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.
Klappentext zu „Weakly Connected Neural Networks “
This book is devoted to local and global analysis of weakly connected systems with applications to neurosciences. Using bifurcation theory and canonical models as the major tools of analysis, it presents systematic and well motivated development of both weakly connected system theory and mathematical neuroscience. Bifurcations in neuron and brain dynamics, synaptic organizations of the brain, and the nature of neural codes are among the many important issues addressed. The authors offer the reader classical results as well as some of the most recent developments in the field. The book will be useful to researchers and graduate students in various branches of mathematical neuroscience.
Inhaltsverzeichnis zu „Weakly Connected Neural Networks “
- Dedication- Preface
- Acknowledgment
- Introduction
- Models in Mathematical Biology
- Ordinary Language Models
- Qualifications
- Dale's Principle
- Weakness of Synaptic Connections
- How small is E?- Size of PSP
- A Common Misinterpretation
- Spike Delays
- Changes of Synaptic Efficacy
- Empirical Models
- Activities of Neurons.
Bibliographische Angaben
- Autoren: Frank C. Hoppensteadt , Eugene M. Izhikevich
- 1997, 402 Seiten, Maße: 16,1 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387949488
- ISBN-13: 9780387949482
Sprache:
Englisch
Rezension zu „Weakly Connected Neural Networks “
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)
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