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Multistability and basin stability in coupled pendulum clocks
Dawid Dudkowski1, Krzysztof Czołczyński1, Tomasz Kapitaniak1
1Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland.
Chaos (Woodbury, N.Y.)
|November 3, 2019
Summary
This study explores multistability and basin stability in coupled pendulum clocks. Mechanical properties of suspension significantly influence attractor types and stability, revealing complex dynamics.
Area of Science:
- Mechanical Engineering
- Nonlinear Dynamics
- Complex Systems
Background:
- Pendulum clocks exhibit complex behaviors like multistability.
- Basin stability is crucial for understanding system predictability.
Purpose of the Study:
- Investigate multistability and basin stability in coupled pendula with escapement mechanisms.
- Analyze synchronization patterns and transitions between different dynamic states.
Main Methods:
- Studied single pendulum clock dynamics.
- Generated basin stability maps by varying stiffness and damping.
- Utilized bifurcation diagrams and basins of attraction maps.
Main Results:
- Observed complete synchronization (inphase, antiphase), practical synchronization, and irregular/chaotic motion.
- Identified complex transitions between different dynamic states.
- Demonstrated that suspension properties critically affect attractor appearance and basin stability.
Conclusions:
- The mechanical properties of the suspension play a vital role in determining system behavior.
- Basin stability is highly dependent on parameter values, leading to potentially unpredictable outcomes.
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