Author | Hoppensteadt, Frank C. author |
---|---|

Title | Weakly Connected Neural Networks [electronic resource] / by Frank C. Hoppensteadt, Eugene M. Izhikevich |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1997 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-1828-9 |

Descript | XVI, 402 p. online resource |

SUMMARY

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 dynamยญ ics of the ith neuron, and gi describes the interactions between neurons. The small parameter โ{130}ฌ indicates the strength of connections between the neurons. Weakly connected systems have attracted much attention since the secยญ ond half of seventeenth century, when Christian Huygens noticed that a pair of pendulum clocks synchronize when they are attached to a lightยญ 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

CONTENT

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

Mathematics
Neurosciences
Mathematical analysis
Analysis (Mathematics)
Biomathematics
Mathematics
Analysis
Mathematical and Computational Biology
Neurosciences