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Time dependent stability margin in multistable systems.

P Brzeski1, J Kurths2, P Perlikowski1

  • 1Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland.

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Summary
This summary is machine-generated.

We developed a new method to analyze complex dynamical systems, identifying critical moments where small disturbances can cause significant changes. This helps predict tipping points in systems like Rössler and Duffing oscillators.

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Area of Science:

  • Non-linear dynamics
  • Complex systems analysis
  • Perturbation theory

Background:

  • Multistable non-linear dynamical systems exhibit complex behaviors.
  • Understanding stability margins is crucial for predicting system responses.
  • Identifying tipping points is essential across various scientific disciplines.

Purpose of the Study:

  • To introduce a novel technique for analyzing the time-dependent stability margin of non-linear dynamical systems.
  • To pinpoint moments along periodic orbits where stability is minimal, indicating potential tipping points.
  • To validate the proposed method through numerical simulations and experimental data.

Main Methods:

  • Characterization of the evolution of a time-dependent stability margin.
  • Application to paradigmatic systems: Rössler and Duffing oscillators.
  • Experimental validation using a double pendulum rig with parametric excitation.

Main Results:

  • The technique successfully characterizes stability margin evolution along periodic orbits.
  • Numerical and experimental results show significant fluctuations in sensitivity to perturbations.
  • Identified critical moments where minimal stability surplus can lead to tipping points.

Conclusions:

  • The proposed method provides a robust tool for analyzing stability in non-linear dynamical systems.
  • It offers valuable insights into predicting tipping points in complex systems.
  • Applicable to diverse fields including engineering, fluid dynamics, climate research, and photonics.