Goal quest for an intelligent surfer moving in a chaotic flow
This work addresses motion control in chaotic flows, offering incremental improvements in pathfinding algorithms for specific dynamical systems.
The authors tackled the problem of finding an optimal path for an intelligent surfer in a chaotic flow modeled by a Ulam network, achieving a logarithmic growth in transitions with network size and exponential outperformance over a naive approach.
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 Erdös 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.