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Updated: Jan 20, 2026
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Traveling amplitude death in coupled pendula
Dawid Dudkowski1, Krzysztof Czołczyński1, Tomasz Kapitaniak1
1Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland.
Chaos (Woodbury, N.Y.)
|September 2, 2019
Summary
Traveling amplitude death (TAD) in coupled pendula with escapement mechanisms is explored. Energy transfer dictates TAD direction, and chaotic dynamics drive its occurrence, often appearing as a random process.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Coupled pendula with escapement mechanisms exhibit complex dynamics.
- Amplitude death is a phenomenon where oscillations cease in coupled systems.
Purpose of the Study:
- To investigate traveling amplitude death (TAD) and stationary amplitude death in coupled pendula with escapement mechanisms.
- To analyze the dynamics, attractors, and energy transfer mechanisms governing TAD.
- To explore the transient dynamics leading to TAD and its relationship with system parameters.
Main Methods:
- Examination of system dynamics in the coupling parameters' plane.
- Analysis of attractors and observed patterns.
- Application of the energy balance method to study energy transfer.
- Investigation of TAD occurrence through perturbation procedures.
- Study of transient pendula behavior and network response.
Main Results:
- The direction of traveling amplitude death is determined by strict energy transfer between pendula.
- Transient dynamics from synchronization to amplitude death are complex and non-straightforward.
- System parameters and perturbation magnitude influence network response during transient processes.
- Traveling amplitude death is linked to chaotic dynamics and appears to result from random processes.
Conclusions:
- Energy transfer is the key mechanism driving the propagation of traveling amplitude death.
- The transition to amplitude death is not a simple process and involves intricate transient dynamics.
- Chaotic dynamics play a crucial role in the emergence of traveling amplitude death, suggesting a stochastic element in its initiation.
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