Mitigating long transient time in deterministic systems by resetting

Abstract

How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest, and has stimulated a lot of activities in dynamical and stochastic systems where the metric of this estimation is often known as the transient or first passage time. In nonlinear systems, one often experiences long transients due to their underlying dynamics. We apply resetting or restart, an emerging concept in statistical physics and stochastic process, to mitigate the detrimental effects of prolonged transients in deterministic dynamical systems. We show that stopping an ongoing process at intermittent time only to restart all over from a spatial control line, can dramatically expedite its completion, resulting in a huge decrease in mean transient time. Moreover, our study unfolds a net reduction in fluctuations around the mean. Our claim is established with detailed numerical studies on the Stuart-Landau limit cycle oscillator and chaotic Lorenz system under different resetting strategies. Our analysis opens up a door to control the mean and fluctuations in transient time by unifying the original dynamics with an external stochastic or periodic timer, and poses open questions on the optimal way to harness transients in dynamical systems.

arXiv comment5 pages, 3 figures in the main text + Supplemental material of 13 pages, 7 figures

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Cited by in corpus (19)

• Stochastic resetting: A (very) brief review
• Extreme events in dynamical systems and random walkers: A review
• The inspection paradox in stochastic resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Extremal statistics for stochastic resetting systems
• Resetting with stochastic return through linear confining potential
• First-passage Brownian functionals with stochastic resetting
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• Universal framework for record ages under restart
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• Multimodal distribution of transient time of predator extinction in a three-species food chain
• Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting
• Chaotic resetting: A resetting strategy for deterministic chaotic systems