Document Type

Article

Original Publication Date

2014

Journal/Book/Conference Title

SIAM Journal on Applied Dynamical Systems

Volume

13

Issue

4

First Page

1733

Last Page

1755

DOI

10.1137/140971099

Comments

AMS subject classifications. 37N25, 92C20

Date of Submission

March 2015

Abstract

Pulse-coupled phase oscillators have been utilized in a variety of contexts. Motivated by neuroscience, we study a network of pulse-coupled phase oscillators receiving independent and correlated noise. An additional physiological attribute, heterogeneity, is incorporated in the phase resetting curve (PRC), which is a vital entity for modeling the biophysical dynamics of oscillators. An accurate probability density or mean field description is large dimensional, requiring reduction methods for tractability. We present a reduction method to capture the pairwise synchrony via the probability density of the phase differences, and explore the robustness of the method. We find the reduced methods can capture some of the synchronous dynamics in these networks. The variance of the noisy period (or spike times) in this network is also considered. In particular, we find phase oscillators with predominately positive PRCs (type 1) have larger variance with inhibitory pulse- coupling than PRCs with a larger negative regions (type 2), but with excitatory pulse-coupling the opposite happens – type 1 oscillators have lower variability than type 2. Analysis of this phenomena is provided via an asymptotic approximation with weak noise and weak coupling, where we demonstrate how the individual PRC alters variability with pulse-coupling. We make comparisons of the phase oscillators to full oscillator networks and discuss the utility and shortcomings.

Rights

© 2014, Society for Industrial and Applied Mathematics. This is the author’s version of a work that was accepted for publication in SIAM J. Appl. Dyn. Syst., 13(4), 1733–1755. The final publication is available at http://dx.doi.org/10.1137/140971099.

Is Part Of

VCU Statistical Sciences and Operations Research Publications

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