Symbolic Dynamics and Chaotic Synchronization in Coupled Duffing Oscillators

In this work we discuss the complete synchronization of two identical double-well Duffing oscillators unidirectionally coupled, from the point of view of symbolic dynamics. Working with Poincaré cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of th...

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Bibliographic Details
Published inJournal of nonlinear mathematical physics Vol. 15; no. sup3; pp. 102 - 111
Main Authors Caneco, Acilina, Grácio, Clara, Rocha, J Leonel
Format Journal Article
LanguageEnglish
Published Dordrecht Taylor & Francis Group 2008
Springer Netherlands
Springer Nature B.V
Subjects
Coupling
Duffing oscillators
Synchronism
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Summary:In this work we discuss the complete synchronization of two identical double-well Duffing oscillators unidirectionally coupled, from the point of view of symbolic dynamics. Working with Poincaré cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized. We obtained analytically the threshold value of the coupling parameter for the synchronization of two unimodal and two bimodal piecewise linear maps, which by semi-conjugacy, under certain conditions, gives us information about the synchronization of the Duffing oscillators.
ISSN:1402-9251
1776-0852
1776-0852
DOI:10.2991/jnmp.2008.15.s3.11