Reliability of Coupled Oscillators

Abstract

We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In this paper, we extend previous results on twocell networks to larger systems. The first issue that arises is chaos in the absence of inputs, which we demonstrate and interpret in terms of reliability. We give a mathematical analysis of networks that can be decomposed into modules connected by an acyclic graph. For this class of networks, we show how to localize the source of unreliability, and address questions concerning downstream propagation of unreliability once it is produced.

Spike-time reliability of layered neural oscillator networks

“…This is an interesting topic in its own right, one that would, however, take us too far afield (see, e.g., Sect. 6 of [33]). The ε = 0.5 curve in Fig.…”

“…In the case λ max = 0, this test is inconclusive. Similar ideas have been used in, e.g., [50,33,40,42].…”

“…Here, we mention prior studies on the effects of feedback and network architecture on neural reliability. The simplest setting in which this was addressed is that of [33], in which reliability was studied for a two-cell analog of the present two-layer system. There, it was found that feedback can lead to unreliability even for this small system; nevertheless, greater feedback strengths could be tolerated in the two-cell network before unreliability was produced.…”

“…Specifically, neural networks experience synaptic variability and failures (synaptic noise) [20,23]; these effects do not arise for direct current injections, as is often done in singlecell studies. Second, network-level interactions can lead to dynamical instabilities which are not present in isolated neurons, causing a network's response to depend sensitively on its internal state at the time of the stimulus is presented [53,50,33,55]. We will attempt to address both of these issues in this paper.…”

“…Previous theoretical studies have addressed the question of reliability on the level of networks: see, e.g., [53,10,36,50,33,5,6]. These and other references on topics related to our work will be discussed in the text as we go along.…”