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Exploring a Terrain with Random Direction Changes

Offered By: Centrum Fizyki Teoretycznej PAN via YouTube

Tags

Stochastic Processes Courses Robotics Courses Differential Equations Courses Mathematical Modeling Courses Random Walks Courses Mean-Field Theory Courses

Course Description

Overview

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Explore a mathematical model of an explorer moving through an inhomogeneous environment in this lecture by Prof. Jan Wehr from the University of Arizona. Delve into a system of stochastic delay equations approximating the explorer's movement, adapting speed to terrain changes with a delay. Examine the limit case where direction changes occur rapidly, and investigate the intriguing possibility of negative delays. Discover how this model applies to light-sensitive mini-robots reacting to local light intensity changes. Analyze the qualitative behavioral shifts occurring at specific delay values and extend findings to swarm behavior through mean field arguments. Learn about the aggregation-deaggregation transition at a critical delay parameter. Gain insights into the mathematical analysis of this problem as a particular case of singular limits in stochastic differential equation systems.

Syllabus

J. Wehr (Dept. of Mathem., University of Arizona): Exploring a terrain with random direction changes


Taught by

Centrum Fizyki Teoretycznej PAN

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