Goal quest for an intelligent surfer moving in a chaotic flow

TL;DR

This paper introduces an algorithm enabling an intelligent surfer to efficiently navigate a complex, chaotic flow network by minimizing resistance, outperforming naive strategies, with potential applications in motion control within chaotic systems.

Contribution

The paper develops a novel algorithm for optimal pathfinding in a chaotic flow network, leveraging fractal intersections and Erdős numbers to improve efficiency over naive methods.

Findings

The algorithm finds paths with a number of transitions growing logarithmically with network size.

The intelligent surfer significantly outperforms naive strategies in reaching the target.

The method offers insights into motion control in chaotic flows.

Abstract

We consider a model of an intelligent surfer moving on the Ulam network generated by a chaotic dynamics in the Chirikov standard map. This directed network is obtained by the Ulam method with a division of the phase space in cells of fixed size forming the nodes of a Markov chain. The goal quest for this surfer is to determine the network path from an initial node A to a final node B with minimal resistance given by the sum of inverse transition probabilities. We develop an algorithm for the intelligent surfer that allows to perform the quest in a small number of transitions which grows only logarithmically with the network size. The optimal path search is done on a fractal intersection set formed by nodes with small Erd\"os numbers of the forward and inverted networks. The intelligent surfer exponentially outperforms a naive surfer who tries to minimize its phase space distance to the target B. We argue that such an algorithm provides new hints for motion control in chaotic flows.