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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/361965
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