Weakly Connected Neural Networks / Edition 1by Frank C. Hoppensteadt, Eugene M. Izhikevich
Pub. Date: 06/04/2008
Publisher: Springer New York
This book develops the bifurcation theory for weakly connected neural networks. The authors analyze the relationship between synaptic organizations (anatomy) and dynamical properties (function) of the brain. In particular the authors show that there are some synaptic organizations that have especially rich dynamic behavior.
Table of Contents1 Introduction.- 2 Bifurcations in Neuron Dynamics.- 3 Neural Networks.- 4 Introduction to Canonical Models.- 5 Local Analysis of WCNNs.- 6 Local Analysis of Singularly Perturbed WCNNs.- 7 Local Analysis of Weakly Connected Maps.- 8 Saddle-Node on a Limit Cycle.- 9 Weakly Connected Oscillators.- 10 Multiple Andronov-Hopf Bifurcation.- 11 Multiple Cusp Bifurcation.- 12 Quasi-Static Bifurcations.- 13 Synaptic Organizations of the Brain.- References.
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