Volume 85, Number 6, March 2009
Article Number 60011
Number of page(s) 5
Section General
Published online 07 April 2009
EPL, 85 (2009) 60011
DOI: 10.1209/0295-5075/85/60011

Master stability functions for coupled nearly identical dynamical systems

J. Sun, E. M. Bollt and T. Nishikawa

Department of Mathematics and Computer Science, Clarkson University - Potsdam, NY 13699-5815, USA

received 21 January 2009; accepted in final form 4 March 2009; published March 2009
published online 7 April 2009

We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves the linear-stability problem for near-synchronous states (NSS) for all possible connectivity structures. We also derive a general sufficient condition for stable near-synchronization and show that the synchronization error scales linearly with the magnitude of parameter variations. Our analysis underlines the significant role played by the Laplacian eigenvectors in the study of network synchronization of near-identical systems.

05.45.Xt - Synchronization; coupled oscillators.
05.45.-a - Nonlinear dynamics and chaos.
89.75.-k - Complex systems.

© EPLA 2009