Introduction to Neural Dynamics and Signal Transmission Delay

by Wu, Jianhong

• ISBN13: 9783110169881
• ISBN10: 3110169886
• Format: Hardcover
• Copyright: 2001-05-01
• Publisher: De Gruyter

Summary

In the design of a neural network, either for biological modeling, cognitive simulation, numerical computation or engineering applications, it is important to investigate the network's computational performance which is usually described by the long-term behaviors, called dynamics, of the model equations. The purpose of this book is to give an introduction to the mathematical modeling and analysis of networks of neurons from the viewpoint of dynamical systems.

Table of Contents

Preface	vii
The structure of neural networks	1	(8)
The structure of single neuron	1	(1)
Transmission of neural signals	2	(5)
Neural circuits, CNS and ANN	7	(2)
Dynamic models of networks	9	(15)
Biological models	9	(5)
Signal functions	14	(2)
General models and network architectures	16	(8)
Simple networks	24	(37)
Outstars: pattern learning	24	(6)
Instars: pattern recognition	30	(4)
Lateral inhibition: noise-saturation dilemma	34	(2)
Recurrent ON-CTR OFF-SUR networks: signal enhancement and noise suppression	36	(14)
Determining synaptic weights	50	(11)
Appendix. Grossberg's Learning Theorem	57	(4)
Content-addressable memory storage	61	(27)
Parallel memory storage by competitive networks	62	(8)
Convergence in networks with a nonsymmetric interconnection matrix	70	(5)
Implementation of CAM: Hopfield networks	75	(4)
Generic convergence in monotone networks	79	(9)
Signal transmissions delays	88	(83)
Neural networks with delay and basic theory	90	(5)
Global stability analysis	95	(4)
Delay - induced instability	99	(6)
Hopf bifurcation of periodic solutions	105	(10)
A network of two neurons: McCulloch-Pitts nonlinearity	115	(23)
Delay-induced transient oscillations	138	(8)
Effect of delay on the basin of attraction	146	(8)
Synchronized activities	154	(11)
Desynchronization, phase-locked oscillation and connecting orbits	165	(6)
Bibliography	171	(8)
Index	179