In this paper, we experimentally verify the phenomenon of chaotic synchronization in coupled forced oscillators. The study is focused on the model of three double pendula locally connected via springs. Each of the individual oscillators can behave both periodically and chaotically, which depends on the parameters of the external excitation (the shaker). We investigate the relation between the strength of coupling between the upper pendulum bobs and the precision of their synchronization, showing that the system can achieve practical synchronization, within which the nodes preserve their chaotic character. We determine the influence of the pendula parameters and the strength of coupling on the synchronization precision, measuring the differences between the nodes’ motion. The results obtained experimentally are confirmed by numerical simulations. We indicate a possible mechanism causing the desynchronization of the system’s smaller elements (lower pendula bobs), which involves their motion around the unstable stationary position and possible transient dynamics. The results presented in this paper may be generalized into typical models of pendula and pendula-like coupled systems, exhibiting chaotic dynamics.
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Experimental chaotic synchronization for coupled double
pendula
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June 2021
Research Article|
June 15 2021
Experimental chaotic synchronization for coupled double
pendula
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Dawid Dudkowski
;
Dawid Dudkowski
a)
Division of Dynamics, Lodz University of Technology
,
Stefanowskiego 1/15, 90-924 Lodz, Poland
a) Author to whom correspondence should be addressed: [email protected]
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Jerzy Wojewoda
;
Jerzy Wojewoda
Division of Dynamics, Lodz University of Technology
,
Stefanowskiego 1/15, 90-924 Lodz, Poland
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Krzysztof Czołczyński
;
Krzysztof Czołczyński
Division of Dynamics, Lodz University of Technology
,
Stefanowskiego 1/15, 90-924 Lodz, Poland
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Tomasz Kapitaniak
Tomasz Kapitaniak
Division of Dynamics, Lodz University of Technology
,
Stefanowskiego 1/15, 90-924 Lodz, Poland
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Dawid Dudkowski
a)
Division of Dynamics, Lodz University of Technology
,
Stefanowskiego 1/15, 90-924 Lodz, Poland
Jerzy Wojewoda
Division of Dynamics, Lodz University of Technology
,
Stefanowskiego 1/15, 90-924 Lodz, Poland
Krzysztof Czołczyński
Division of Dynamics, Lodz University of Technology
,
Stefanowskiego 1/15, 90-924 Lodz, Poland
Tomasz Kapitaniak
Division of Dynamics, Lodz University of Technology
,
Stefanowskiego 1/15, 90-924 Lodz, Poland
a) Author to whom correspondence should be addressed: [email protected]
Chaos 31, 061107 (2021)
Article history
Received:
May 11 2021
Accepted:
May 28 2021
Citation
Dawid Dudkowski, Jerzy Wojewoda, Krzysztof Czołczyński, Tomasz Kapitaniak; Experimental chaotic synchronization for coupled double pendula. Chaos 1 June 2021; 31 (6): 061107. https://doi.org/10.1063/5.0056530
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