Reverberating activity in a neural network with distributed signal transmission delays

TL;DR

This paper investigates how distributed transmission delays in neural networks lead to collective oscillations, reverberating activity, and complex dynamics such as quasiperiodicity and chaos.

Contribution

It introduces a model of neural networks with distributed delays and analyzes how these delays influence collective oscillations and complex behaviors.

Findings

Networks exhibit a collective oscillation close to the average delay

Distributed delays can produce reverberating, nontrivial firing sequences

Changing delay distribution induces quasiperiodic or chaotic dynamics

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.