Small-world networks exhibit pronounced intermittent synchronization
| Autor: | Chiranjit Mitra, Jürgen Kurths, Anshul Choudhary, Vivek Kohar, Sudeshna Sinha |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Lyapunov function
Applied Mathematics General Physics and Astronomy Statistical and Nonlinear Physics Lyapunov exponent Topology Dynamical system 01 natural sciences Stability (probability) Synchronization 010305 fluids & plasmas law.invention Nonlinear Sciences::Chaotic Dynamics symbols.namesake Control theory law Intermittency 0103 physical sciences symbols 010306 general physics Mathematical Physics Master stability function Mathematics Linear stability |
| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science. 27:111101 |
| ISSN: | 1089-7682 1054-1500 |
| DOI: | 10.1063/1.5002883 |
| Popis: | We report the phenomenon of temporally intermittently synchronized and desynchronized dynamics in Watts-Strogatz networks of chaotic Rössler 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. |
| Databáze: | OpenAIRE |
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