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Weakly Connected Neural Networks / by Frank C. Hoppensteadt, Eugene M. Izhikevich
(Applied Mathematical Sciences. ISSN:2196968X ; 126)
版 | 1st ed. 1997. |
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出版者 | (New York, NY : Springer New York : Imprint: Springer) |
出版年 | 1997 |
本文言語 | 英語 |
大きさ | XVI, 402 p : online resource |
著者標目 | *Hoppensteadt, Frank C author Izhikevich, Eugene M author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Biomathematics LCSH:Neurosciences FREE:Analysis FREE:Mathematical and Computational Biology FREE:Neuroscience |
一般注記 | 1 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 This book is devoted to an analysis of general weakly connected neural networks (WCNNs) that can be written in the form (0.1) m Here, each Xi E IR is a vector that summarizes all physiological attributes of the ith neuron, n is the number of neurons, Ii describes the dynam ics of the ith neuron, and gi describes the interactions between neurons. The small parameter € indicates the strength of connections between the neurons. Weakly connected systems have attracted much attention since the sec ond half of seventeenth century, when Christian Huygens noticed that a pair of pendulum clocks synchronize when they are attached to a light weight beam instead of a wall. The pair of clocks is among the first weakly connected systems to have been studied. Systems of the form (0.1) arise in formal perturbation theories developed by Poincare, Liapunov and Malkin, and in averaging theories developed by Bogoliubov and Mitropolsky HTTP:URL=https://doi.org/10.1007/978-1-4612-1828-9 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781461218289 |
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EB00227142 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000105395 |
ISBN | 9781461218289 |
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