Effect of node-degree correlation on synchronization of identical pulse-coupled oscillators.
We explore the effect of correlations between the in and out degrees of random directed networks on the synchronization of identical pulse-coupled oscillators. Numerical experiments demonstrate that the proportion of initial conditions resulting in a globally synchronous state (prior to a large but finite time) is an increasing function of node-degree correlation. For those networks observed to globally synchronize, both the mean and standard deviation of time to synchronization are decreasing functions of node-degree correlation. Pulse-coupled oscillator networks with negatively correlated node degree often exhibit multiple coherent attracting states, with trajectories performing fast transitions between them. These effects of node-degree correlation on dynamics of pulse-coupled oscillators are consistent with aspects of network topology (e.g., the effect of node-degree correlation on the eigenvalues of the Laplacian matrix) that have been shown to affect synchronization in other contexts.
LaMar
M Drew
MD
Department of Applied Science, The College of William and Mary, McGlothlin-Street Hall, Williamsburg, Virginia 23187, USA. mdlama@wm.edu
Smith
Gregory D
GD
D042541:Intracellular Space / Q000378:metabolism; D008954:Models, Biological; D008962:Models, Theoretical; D009415:Nerve Net / Q000166:cytology / Q000502:physiology