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Shear Diversity Prevents Collective Synchronization Ernest Montbrio1

Summary: Shear Diversity Prevents Collective Synchronization
Ernest Montbrio´1
and Diego Pazo´2
Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain
Instituto de Fi´sica de Cantabria (IFCA), CSIC-Universidad de Cantabria, 39005 Santander, Spain
(Received 21 February 2011; published 21 June 2011)
Large ensembles of heterogeneous oscillators often exhibit collective synchronization as a result of
mutual interactions. If the oscillators have distributed natural frequencies and common shear (or
nonisochronicity), the transition from incoherence to collective synchronization is known to occur at
large enough values of the coupling strength. However, here we demonstrate that shear diversity cannot be
counterbalanced by diffusive coupling leading to synchronization. We present the first analytical results
for the Kuramoto model with distributed shear and show that the onset of collective synchronization is
impossible if the width of the shear distribution exceeds a precise threshold.
DOI: 10.1103/PhysRevLett.106.254101 PACS numbers: 05.45.Xt
Collective synchronization is a form of self-organization
in time that results from the interactions among a large
heterogeneous population of self-sustained oscillators
[1­5]. This phenomenon is observed in a large variety of


Source: Andrzejak, Ralph Gregor - Departament de Tecnologia, Universitat Pompeu Fabra
Deco, Gustavo - Departament de Tecnologia, Universitat Pompeu Fabra


Collections: Computer Technologies and Information Sciences