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.
Skip Nav Destination
Article navigation
June 2023
Research Article|
June 21 2023
Coupled pendula with varied forcing direction Available to Purchase
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
Search for other works by this author on:
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: [email protected]
Search for other works by this author on:
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:
Dawid Dudkowski
Conceptualization, Formal analysis, Investigation, Writing – original draft
Division of Dynamics, Lodz University of Technology
, Stefanowskiego 1/15, 90-924 Lodz, Poland
Patrycja Jaros
Conceptualization, Formal analysis, Investigation, Writing – original draft
a)
Division of Dynamics, Lodz University of Technology
, Stefanowskiego 1/15, 90-924 Lodz, Poland
Tomasz Kapitaniak
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: [email protected]
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
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto–Sivashinsky test case
Rambod Mojgani, Ashesh Chattopadhyay, et al.
Recent achievements in nonlinear dynamics, synchronization, and networks
Dibakar Ghosh, Norbert Marwan, et al.
Enhancing reservoir predictions of chaotic time series by incorporating delayed values of input and reservoir variables
Luk Fleddermann, Sebastian Herzog, et al.
Related Content
Mixed-mode chimera states in pendula networks
Chaos (October 2022)
Traveling amplitude death in coupled pendula
Chaos (August 2019)
Synchronization and decoherence in a self-excited inertia-wheel multiple rigid-body dynamical system
Chaos (December 2023)
Synchronous rotation of the set of double pendula: Experimental observations
Chaos (December 2012)
Experimental chaotic synchronization for coupled double
pendula
Chaos (June 2021)