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Titlebook: Weakly Connected Neural Networks; Frank C. Hoppensteadt,Eugene M. Izhikevich Book 1997 Springer Science+Business Media New York 1997 biolo

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书目名称Weakly Connected Neural Networks
编辑Frank C. Hoppensteadt,Eugene M. Izhikevich
视频video
概述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
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Weakly Connected Neural Networks;  Frank C. Hoppensteadt,Eugene M. Izhikevich Book 1997 Springer Science+Business Media New York 1997 biolo
描述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.
出版日期Book 1997
关键词biology; calculus; differential equation; neural network; neurons; neuroscience
版次1
doihttps://doi.org/10.1007/978-1-4612-1828-9
isbn_softcover978-1-4612-7302-8
isbn_ebook978-1-4612-1828-9Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer Science+Business Media New York 1997
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发表于 2025-3-22 00:17:20 | 显示全部楼层
https://doi.org/10.1007/978-1-4612-1828-9biology; calculus; differential equation; neural network; neurons; neuroscience
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Weakly Connected Neural Networks978-1-4612-1828-9Series ISSN 0066-5452 Series E-ISSN 2196-968X
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IntroductionIn this chapter we give definitions and explanations of basic neurophysio­logical terminology that we use in the book. We do not intend to provide a comprehensive background on various topics.
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Saddle-Node on a Limit CycleIn this chapter we study a weakly connected network . of neurons each having a saddle-node bifurcation on a limit cycle. Such neurons are said to have Class 1 neural excitability. This bifurcation provides an important example of when local analysis at an equilibrium renders global information about the system behavior.
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Quasi-Static BifurcationsIn this chapter we analyze the canonical models (6.17) and (6.24) for singu­larly perturbed WCNNs at quasi-static saddle-node and quasi-static cusp bifurcations. In particular, we consider the canonical models in the special case ..
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Synaptic Organizations of the BrainIn this chapter we study the relationship between synaptic organizations and dynamical properties of networks of neural oscillators. In particular, we are interested in which synaptic organizations can memorize and reproduce phase information. Most of our results are obtained for neural oscillators near multiple Andronov-Hopf bifurcations.
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