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Multistability and basin stability in coupled pendulum clocks.

Dawid Dudkowski1, Krzysztof Czołczyński1, Tomasz Kapitaniak1

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Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study explores multistability and basin stability in coupled pendulum clocks. Mechanical properties of suspension significantly influence attractor types and stability, revealing complex dynamics.

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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.