Confinement-controlled chase-escape dynamics

TL;DR

This study explores how geometric disorder and percolation influence chase-and-escape dynamics on a lattice, revealing a transition from cooperative pursuit to confinement-dominated trapping governed by connectivity.

Contribution

It introduces a minimal chase-and-escape model incorporating obstacle-induced connectivity effects, linking lattice fragmentation to pursuit efficiency and trapping behavior.

Findings

Obstacle density affects pursuit success and trapping times.

Survivor decay follows Weibull distribution with density-dependent parameters.

Transport exhibits sub-diffusive behavior near percolation threshold.

Abstract

We investigate a minimal chase-and-escape model on a two-dimensional square lattice with randomly distributed static obstacles, focusing on how geometric disorder controls collective pursuit dynamics. Chasers and escapers move according to short-range sensing rules, while the density of obstacles tunes the connectivity of the accessible space. Using a combination of geometric analysis, dynamical observables, survival statistics, and transport characterization, we establish a direct link between lattice connectivity and pursuit efficiency. A Breadth-First Search analysis reveals that obstacle-induced fragmentation leads to a progressive loss of accessibility before the percolation threshold, defining the effective initial conditions for the dynamics. The trapping time and capture cost exhibit a non-monotonic dependence on obstacle density, reflecting a competition between path elongation in connected environments and geometric confinement near the percolation threshold. Survival analysis shows that the decay of the escaper population follows a Weibull form, with characteristic time and shape parameters displaying clear crossovers as a function of obstacle density, signaling the coexistence of cooperative capture and confinement-dominated trapping. Transport properties, quantified through the mean-squared displacement exponent, further support this picture, revealing sub-diffusive dynamics and a convergence toward a geometry-controlled regime near percolation. Overall, our results demonstrate that chase--and--escape dynamics in disordered environments are governed by a geometry-driven crossover, where percolation and connectivity act as unifying control parameters for spatial, temporal, and collective behavior.