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Mitigating long transient time in deterministic systems by resetting.

Arnob Ray1, Arnab Pal2, Dibakar Ghosh1

  • 1Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.

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

Resetting dynamical systems can significantly shorten the time trajectories take to reach equilibrium. This study finds an optimal restart time that minimizes this transient time, offering new control methods.

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Area of Science:

  • Physics
  • Mathematics
  • Complex Systems

Background:

  • Estimating the time for a dynamical system trajectory to reach equilibrium (transient time) is crucial.
  • Nonlinear systems often exhibit prolonged transients, posing challenges for analysis and control.

Purpose of the Study:

  • To investigate the use of resetting (intermittent restarts) to reduce long transient times in deterministic dynamical systems.
  • To identify an optimal resetting strategy for minimizing mean transient time.

Main Methods:

  • Applying intermittent resetting to the intrinsic dynamics of systems.
  • Analyzing the impact of resetting on transient time and its fluctuations.
  • Conducting numerical simulations on the Stuart-Landau oscillator and the Lorenz system.

Main Results:

  • Resetting dramatically expedites the completion of trajectories, significantly reducing mean transient time.
  • An optimal restart time was identified that globally minimizes the mean transient time.
  • The effectiveness of resetting was found to be generic across different resetting strategies and systems.

Conclusions:

  • Resetting is a powerful technique to control and reduce transient times in deterministic dynamical systems.
  • This approach offers a novel way to manage system dynamics by combining intrinsic behavior with external timers.
  • Further research is needed to explore optimal harnessing of transients in complex systems.