Predicting synchrony in heterogeneous pulse coupled oscillators.
Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.
Talathi
Sachin S
SS
J. Crayton Pruitt Department of Biomedical Engineering, University of Florida, Gainesville, Florida 32611, USA. sachin.talathi@bme.ufl.edu
Hwang
Dong-Uk
DU
Miliotis
Abraham
A
Carney
Paul R
PR
Ditto
William L
WL
D008959:Models, Neurological; D009474:Neurons / Q000166:cytology; D017711:Nonlinear Dynamics; D013569:Synapses / Q000378:metabolism