In this paper, we investigate the complex dynamics of rotating pendula arranged into a simple mechanical scheme. Three nodes forming the small network are coupled via the horizontally oscillating beam (the global coupling structure) and the springs (the local coupling), which extends the research performed previously for similar models. The pendula rotate in different directions, and depending on the distribution of the latter ones, various types of behaviors of the system can be observed. We determine the regions of the existence and co-existence of particular solutions using both the classical method of bifurcations, as well as a modern sample-based approach based on the concept of basin stability. Various types of states are presented and discussed, including synchronization patterns, coherent dynamics, and irregular motion. We uncover new schemes of solutions, showing that both rotations and oscillations can co-exist for various pendula, arranged within one common system. Our analysis includes the investigations of the basins of attraction of different dynamical patterns, as well as the study on the properties of the observed states, along with the examination of the influence of system’s parameters on their behavior. We show that the model can respond in spontaneous ways and uncover unpredicted irregularities occurring for the states. Our study exhibits that the inclusion of the local coupling structure can induce complex, chimeric dynamics of the system, leading to new co-existing patterns for coupled mechanical nodes.
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June 2023
Research Article|
June 21 2023
Coupled pendula with varied forcing direction
Special Collection:
Chimera states: from theory and experiments to technology and living systems
Dawid Dudkowski
;
Dawid Dudkowski
(Conceptualization, Formal analysis, Investigation, Writing – original draft)
Division of Dynamics, Lodz University of Technology
, Stefanowskiego 1/15, 90-924 Lodz, Poland
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Patrycja Jaros
;
Patrycja Jaros
a)
(Conceptualization, Formal analysis, Investigation, Writing – original draft)
Division of Dynamics, Lodz University of Technology
, Stefanowskiego 1/15, 90-924 Lodz, Poland
a)Author to whom correspondence should be addressed: patrycja.kuzma@p.lodz.pl
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Tomasz Kapitaniak
Tomasz Kapitaniak
(Conceptualization, Formal analysis, Investigation, Writing – original draft)
Division of Dynamics, Lodz University of Technology
, Stefanowskiego 1/15, 90-924 Lodz, Poland
Search for other works by this author on:
a)Author to whom correspondence should be addressed: patrycja.kuzma@p.lodz.pl
Note: This paper is part of the Focus Issue on Chimera states from theory and experiments to technology and living systems.
Chaos 33, 063142 (2023)
Article history
Received:
February 03 2023
Accepted:
May 31 2023
Citation
Dawid Dudkowski, Patrycja Jaros, Tomasz Kapitaniak; Coupled pendula with varied forcing direction. Chaos 1 June 2023; 33 (6): 063142. https://doi.org/10.1063/5.0145165
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