Networks of nonlinear dynamical systems may exhibit a collective state, known as cluster synchronization, characterized by the formation of groups, where the units within each cluster converge to the same behavior that is distinct for each cluster. In this brief paper we derive a criterion for local stability in Milnor sense of this synchronous state that is expressed as a simple relationship between the maximum Lyapunov exponent of the uncoupled dynamics, the coupling coefficient, and one eigenvalue of the graph Laplacian spectrum. In the last part of the paper we discuss the application of the criterion to networks design and control.
A criterion for stability of cluster synchronization in networks with external equitable partitions
Gambuzza, Lucia Valentina;Frasca, Mattia
2019-01-01
Abstract
Networks of nonlinear dynamical systems may exhibit a collective state, known as cluster synchronization, characterized by the formation of groups, where the units within each cluster converge to the same behavior that is distinct for each cluster. In this brief paper we derive a criterion for local stability in Milnor sense of this synchronous state that is expressed as a simple relationship between the maximum Lyapunov exponent of the uncoupled dynamics, the coupling coefficient, and one eigenvalue of the graph Laplacian spectrum. In the last part of the paper we discuss the application of the criterion to networks design and control.File | Dimensione | Formato | |
---|---|---|---|
1-s2.0-S0005109818305582-A criterion for stability of cluster synchronization.pdf
solo gestori archivio
Tipologia:
Versione Editoriale (PDF)
Dimensione
885.07 kB
Formato
Adobe PDF
|
885.07 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.