Modelling interactions between active and passive agents moving through heterogeneous environments

TL;DR

This paper models the complex interactions between active and passive agents in heterogeneous environments, revealing how their interplay influences system dynamics and residence times through new mathematical models and simulations.

Contribution

It introduces two novel models for mixed active-passive agent systems, providing qualitative analysis and mathematical insights into their well-posedness and dynamics.

Findings

Residence times are significantly affected by interactions between populations.

The models demonstrate how local interactions influence overall system behavior.

Mathematical analysis confirms the models' well-posedness.

Abstract

We study the dynamics of interacting agents from two distinct inter-mixed populations: One population includes active agents that follow a predetermined velocity field, while the second population contains exclusively passive agents, i.e. agents that have no preferred direction of motion. The orientation of their local velocity is affected by repulsive interactions with the neighboring agents and environment. We present two models that allow for a qualitative analysis of these mixed systems. We show that the residence times of this type of systems containing mixed populations is strongly affected by the interplay between these two populations. After showing our modeling and simulation results, we conclude with a couple of mathematical aspects concerning the well-posedness of our models.