Reverberating activity in a neural network with distributed signal transmission delays
Abstract
It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are distributed in time. Here, a neuron is modeled as a discrete-time threshold element that responds in an all-or-nothing manner to a linear sum of signals that arrive after delays assigned to individual transmission lines. Even though transmission delays are distributed in time, a whole network exhibits a single collective oscillation with a period close to the average transmission delay. The collective oscillation can not only be a simple alternation of the consecutive firing and resting, but also nontrivially sequenced series of firing and resting, reverberating in a certain period of time. Moreover, the system dynamics can be made quasiperiodic or chaotic by changing the distribution of delays.
Cite
@article{arxiv.0708.0606,
title = {Reverberating activity in a neural network with distributed signal transmission delays},
author = {Takahiro Omi and Shigeru Shinomoto},
journal= {arXiv preprint arXiv:0708.0606},
year = {2011}
}
Comments
8pages, 9figures