Phase response curves, delays and synchronization in Matlab

Abstract

MatCont is a Matlab software package for the study of dynamical systems. We extended this package with the functionality of computing the phase response curve or PRO of a neural model. An important application lies in the study of synchronization of neurons. In synchronization studies, often the delays in a network are discarded or set to zero. We show in this paper that the delay can be crucial for the ability of neurons in an excitatory network to synchronize. We also show that, by studying the PRO of a neural model, one can compute the necessary delay to allow synchronization or phase-locking in a network of such neurons. © Springer-Verlag Berlin Heidelberg 2006.