Dynamics and Steady States in excitable mobile agent systems

TL;DR

This paper investigates how excitation spreads and reaches steady states in 2D mobile agent systems, revealing that agent dynamics and contact rates critically influence the excitation regimes and steady-state populations.

Contribution

It introduces a detailed analysis of excitation dynamics in mobile agents, highlighting the impact of contact rate and exposition time coupling on steady states and identifying three distinct regimes.

Findings

No excitation at low contact rates

Inverse proportionality of excited agents to contact rate in intermediate regime

Scaling law for steady-state quiescent agents at high contact rates

Abstract

We study the spreading of excitations in 2D systems of mobile agents where the excitation is transmitted when a quiescent agent keeps contact with an excited one during a non-vanishing time. We show that the steady states strongly depend on the spatial agent dynamics. Moreover, the coupling between exposition time ($\omega$) and agent-agent contact rate (CR) becomes crucial to understand the excitation dynamics, which exhibits three regimes with CR: no excitation for low CR, an excited regime in which the number of quiescent agents (S) is inversely proportional to CR, and for high CR, a novel third regime, model dependent, here S scales with an exponent $\xi -1$, with $\xi$ being the scaling exponent of $\omega$ with CR.