Master stability functions for coupled nearly identical dynamical systems

By Jie Sun, Erik M. Bollt, Takashi Nishikawa. 2008

171 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/79a5a2c799bc1b6a0c1be7e6e9d1e67c7d031eca

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings (2014, unknown): “Measuring Information Transfer in Two Coupled Oscillators Coupled oscillator networks are commonly used for modeling the dynamic behavior of complex systems in various areas [23, 24, 25, 26].”
Spontaneous synchrony in power-grid networks (2013, background): “More important, even when the βi values are not identical, as in the case of real power grids, adjusting Ri according to equation (11) or Di according to equation (12) in general results in substantially improved stability.”
The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives (2024, background): “Although it is possible to compensate for this heterogeneity to some degree (while accepting other constraining assumptions) (Sun et al., 2009; Nishikawa and Motter, 2010; Zhang and Motter, 2017), a global synchronization state is fortunately not achieved in the brain (and would indicate complete…”