Weakly Connected Neural
Networks by F.C. Hoppensteadt and
E.M. Izhikevich

ISBN 0-387-94948-8, 1997, 400 pages, 173 illustrations, $49.95 (as of 1997)

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The 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 a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience.

Bifurcations in neuron and brain dynamics, oscillatory neural networks, 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.

Preface (Postscript file 105K, gzip 35K)
Part I. Introduction
Chapter 1. Introduction (Postscript file 3.73M, gzip 161K)
Chapter 2. Bifurcations in Neuron Dynamics (Postsript file 1.51M, gzip 360K)
Chapter 3. Neural Networks
Chapter 4. Introduction to Canonical Models
Part II. Derivation of Canonical Models
Chapter 5. Local Analysis of WCNNs
Chapter 6. Local Analysis of Singularly Perturbed WCNNs
Chapter 7. Local Analysis of Weakly Connected Maps
Chapter 8. Saddle-Node on a Limit Cycle
Chapter 9. Weakly Connected Oscillators
Part III. Analysis of Canonical Models
Chapter 10. Multiple Andronov-Hopf Bifurcation
Chapter 11. Multiple Cusp Bifurcation
Chapter 12. Quasi-Static Bifurcations
Chapter 13. Synaptic Organizations of the Brain

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