Symmetry- and input-cluster synchronization in networks

Abu Bakar Siddique, Louis Pecora, Joseph D. Hart, and Francesco Sorrentino

Phys. Rev. E 97, 042217 – Published 25 April 2018

Abstract

We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital partitions of the network nodes (symmetry-cluster synchronization) and equitable partitions of the network nodes (input-cluster synchronization). Our results are verified experimentally in networks of coupled optoelectronic oscillators.

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Received 28 December 2017
Revised 20 February 2018

DOI:https://doi.org/10.1103/PhysRevE.97.042217

Physics Subject Headings (PhySH)

Bifurcations Chimera states Complex systems Coupled oscillators Dynamics of networks Network structure Synchronization

Nonlinear DynamicsNetworksInterdisciplinary Physics

Authors & Affiliations

Abu Bakar Siddique¹, Louis Pecora², Joseph D. Hart³, and Francesco Sorrentino¹

¹Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
²Code 6343, U.S. Naval Research Laboratory, Washington, DC 20375, USA
³Department of Physics, University of Maryland, College Park, College Park, Maryland 20742, USA

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Issue

Vol. 97, Iss. 4 — April 2018

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics