Chaotic resetting: A resetting strategy for deterministic chaotic systems

TL;DR

This paper introduces chaotic resetting, a novel strategy for deterministic chaotic systems that leverages initial condition sensitivity to improve search efficiency, showing significant reductions in search times under optimal resetting intervals.

Contribution

It proposes chaotic resetting as a new method for accelerating searches in chaotic systems, connecting chaos theory with optimization strategies.

Findings

Chaotic resetting can significantly reduce average search times.

Optimal resetting intervals are crucial for effectiveness.

Mixed phase space is necessary for advantages to manifest.

Abstract

Restarting a stochastic search process can accelerate its completion by providing an opportunity to take a more favorable path with each reset. This strategy, known as stochastic resetting, is well studied in random processes. Here, we introduce chaotic resetting, a fundamentally different resetting strategy designed for deterministic chaotic systems. Unlike stochastic resetting, where randomness is intrinsic to the dynamics, chaotic resetting exploits the extreme sensitivity to initial conditions inherent to chaotic motion: unavoidable uncertainties in the reset conditions effectively generate new realizations of the deterministic process. This extension is nontrivial because some realizations may significantly speed up the search, while others may significantly slow it down. We study the conditions required for chaotic resetting to be consistently advantageous, concluding that it requires the presence of a mixed phase space in which fractal and smooth regions coexist. We quantify its effectiveness by demonstrating substantial reductions in average search times when an optimal resetting interval is used. These results establish a clear conceptual bridge between deterministic chaos and search optimization, opening new avenues for accelerating processes in real-world chaotic systems where perfect control or knowledge of initial conditions is unattainable.