Building bridges Lévy-walk way

Speaker: Prof. Dr. Vasily Zaburdaev
Affiliation: FAU Erlangen-Nürnberg (Germany)
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)

Zoom meeting link
Meeting ID: 679 0590 6762 | PIN: 800866

Abstract. Lévy walks are random walks in which the walker moves continuously and with a constant velocity between the reorientation events. The durations of these displacements and correspondingly their lengths are power-law distributed. Lévy walks were shown to be a very successful model to describe a variety of anomalous diffusion dispersal phenomena in physics, biology and ecology. In the context of search, Lévy walks were suggested as an optimal strategy for finding rare renewable targets and that boosted the research in Lévy foraging strategies in living organisms. The trend was inherited in robotics, where Lévy algorithms were implemented in robots performing various search tasks.

However, one important aspect intrinsically present in most living systems but also in robotics – the existence of home range – was not considered before in the context of random search. The fact that a bird needs to return to its nest and a robot to its charging station seems obvious, but the implementation of such processes on the model level is a highly non-trivial task. In this talk, we will introduce the concept of Lévy walk bridges – Lévy walk trajectories returning to the origin after a fixed time. We will show how to tackle the challenge of the efficient bridge generation and how the Lévy walk bridges operate during search. We will discuss what further intriguing problems open up in relation to the introduced concept.