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Title: Synchronizing noisy nonidentical oscillators by transient uncoupling

Abstract

Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them—a phenomenon termed “generalized synchronization.” Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.

Authors:
;  [1];  [2];  [2];  [3];  [1];  [4]
  1. Department of Physics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016 (India)
  2. Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany)
  3. (Germany)
  4. (India)
Publication Date:
OSTI Identifier:
22596516
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 9; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; CHAOS THEORY; NOISE; ORBITS; OSCILLATORS; PHASE SPACE; SYNCHRONIZATION; TRAJECTORIES; TRANSIENTS

Citation Formats

Tandon, Aditya, E-mail: adityat@iitk.ac.in, Mannattil, Manu, E-mail: mmanu@iitk.ac.in, Schröder, Malte, E-mail: malte@nld.ds.mpg.de, Timme, Marc, E-mail: timme@nld.ds.mpg.de, Department of Physics, Technical University of Darmstadt, 64289 Darmstadt, Chakraborty, Sagar, E-mail: sagarc@iitk.ac.in, and Mechanics and Applied Mathematics Group, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016. Synchronizing noisy nonidentical oscillators by transient uncoupling. United States: N. p., 2016. Web. doi:10.1063/1.4959141.
Tandon, Aditya, E-mail: adityat@iitk.ac.in, Mannattil, Manu, E-mail: mmanu@iitk.ac.in, Schröder, Malte, E-mail: malte@nld.ds.mpg.de, Timme, Marc, E-mail: timme@nld.ds.mpg.de, Department of Physics, Technical University of Darmstadt, 64289 Darmstadt, Chakraborty, Sagar, E-mail: sagarc@iitk.ac.in, & Mechanics and Applied Mathematics Group, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016. Synchronizing noisy nonidentical oscillators by transient uncoupling. United States. doi:10.1063/1.4959141.
Tandon, Aditya, E-mail: adityat@iitk.ac.in, Mannattil, Manu, E-mail: mmanu@iitk.ac.in, Schröder, Malte, E-mail: malte@nld.ds.mpg.de, Timme, Marc, E-mail: timme@nld.ds.mpg.de, Department of Physics, Technical University of Darmstadt, 64289 Darmstadt, Chakraborty, Sagar, E-mail: sagarc@iitk.ac.in, and Mechanics and Applied Mathematics Group, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016. Thu . "Synchronizing noisy nonidentical oscillators by transient uncoupling". United States. doi:10.1063/1.4959141.
@article{osti_22596516,
title = {Synchronizing noisy nonidentical oscillators by transient uncoupling},
author = {Tandon, Aditya, E-mail: adityat@iitk.ac.in and Mannattil, Manu, E-mail: mmanu@iitk.ac.in and Schröder, Malte, E-mail: malte@nld.ds.mpg.de and Timme, Marc, E-mail: timme@nld.ds.mpg.de and Department of Physics, Technical University of Darmstadt, 64289 Darmstadt and Chakraborty, Sagar, E-mail: sagarc@iitk.ac.in and Mechanics and Applied Mathematics Group, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016},
abstractNote = {Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them—a phenomenon termed “generalized synchronization.” Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.},
doi = {10.1063/1.4959141},
journal = {Chaos (Woodbury, N. Y.)},
number = 9,
volume = 26,
place = {United States},
year = {Thu Sep 15 00:00:00 EDT 2016},
month = {Thu Sep 15 00:00:00 EDT 2016}
}