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Spatiotemporal Pattern Formation in a Ring of Chua’s Oscillators

Spatiotemporal Pattern Formation in a Ring of Chua’s Oscillators In the present work the spontaneous dynamics of a ring of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N$$\end{document} Chua’s oscillators, mutually coupled through a resistor \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R_{c}$$\end{document} in anearest-neighbor configuration, is investigated numerically for different strengths of the coupling. A transition from periodic to chaoticglobal dynamics is observed when the coupling decreases below a critical value and complex patterns in the spatiotemporal dynamics of thering emerge for a small coupling interval after the transition to chaos. The recovered behavior, as well asthe value of the criticalthreshold, appears to be independent of the size of the ring. We also propose aninterpretation of this property, which relates the regularsynchronized dynamics of the ring to the dynamics of the isolated oscillator. Finally,for the ring of the coupled oscillator, a theoretical wavedispersion relation is calculated and successfully compared with the results of thenumerical simulations, analyzed by classicaltechniques adopted for turbulent flows. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

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Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2021
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/s1560354721060095
Publisher site
See Article on Publisher Site

Abstract

In the present work the spontaneous dynamics of a ring of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N$$\end{document} Chua’s oscillators, mutually coupled through a resistor \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R_{c}$$\end{document} in anearest-neighbor configuration, is investigated numerically for different strengths of the coupling. A transition from periodic to chaoticglobal dynamics is observed when the coupling decreases below a critical value and complex patterns in the spatiotemporal dynamics of thering emerge for a small coupling interval after the transition to chaos. The recovered behavior, as well asthe value of the criticalthreshold, appears to be independent of the size of the ring. We also propose aninterpretation of this property, which relates the regularsynchronized dynamics of the ring to the dynamics of the isolated oscillator. Finally,for the ring of the coupled oscillator, a theoretical wavedispersion relation is calculated and successfully compared with the results of thenumerical simulations, analyzed by classicaltechniques adopted for turbulent flows.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Nov 1, 2021

Keywords: coupled nonlinear oscillators; Chua oscillator; Patterns formation; ordinary differential equations; bifurcation

References