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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.)
|March 23, 2021
Summary
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.
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.
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