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Small-world networks exhibit pronounced intermittent synchronization

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Choudhary, Anshul [1] ; Mitra, Chiranjit [2, 3] ; Kohar, Vivek [4] ; Sinha, Sudeshna [5] ; Kurths, Juergen [2, 3]
Total Authors: 5
[1] Carl von Ossietzky Univ Oldenburg, Theoret Phys Complex Syst, ICBM, D-26111 Oldenburg - Germany
[2] Humboldt Univ, Dept Phys, D-12489 Berlin - Germany
[3] Potsdam Inst Climate Impact Res, Res Domain Transdisciplinary Concepts & Methods 4, D-14473 Potsdam - Germany
[4] Jackson Lab, Bar Harbor, ME 04609 - USA
[5] Indian Inst Sci Educ & Res IISER Mohali, Sect 81, PO 140 306, Manauli, Punjab - India
Total Affiliations: 5
Document type: Journal article
Source: Chaos; v. 27, n. 11 NOV 2017.
Web of Science Citations: 0

We report the phenomenon of temporally intermittently synchronized and desynchronized dynamics in Watts-Strogatz networks of chaotic Roossler oscillators. We consider topologies for which the master stability function (MSF) predicts stable synchronized behaviour, as the rewiring probability (p) is tuned from 0 to 1. MSF essentially utilizes the largest non-zero Lyapunov exponent transversal to the synchronization manifold in making stability considerations, thereby ignoring the other Lyapunov exponents. However, for an N-node networked dynamical system, we observe that the difference in its Lyapunov spectra (corresponding to the N - 1 directions transversal to the synchronization manifold) is crucial and serves as an indicator of the presence of intermittently synchronized behaviour. In addition to the linear stability-based (MSF) analysis, we further provide global stability estimate in terms of the fraction of state-space volume shared by the intermittently synchronized state, as p is varied from 0 to 1. This fraction becomes appreciably large in the small-world regime, which is surprising, since this limit has been otherwise considered optimal for synchronized dynamics. Finally, we characterize the nature of the observed intermittency and its dominance in state-space as network rewiring probability (p) is varied. Published by AIP Publishing. (AU)

Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants