dorsal/arxiv
View SchemaConfinement-controlled chase-escape dynamics
| Authors | R. G. Rossatto, H. Ariel Alvarez, C. Manuel Carlevaro, José Rafael Bordin |
|---|---|
| Categories | |
| ArXiv ID | 2601.06291vv1 |
| URL | https://arxiv.org/abs/2601.06291 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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.
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"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.",
"arxiv_id": "2601.06291",
"authors": [
"R. G. Rossatto",
"H. Ariel Alvarez",
"C. Manuel Carlevaro",
"Jos\u00e9 Rafael Bordin"
],
"categories": [
"cond-mat.stat-mech",
"physics.app-ph"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Confinement-controlled chase-escape dynamics",
"url": "https://arxiv.org/abs/2601.06291",
"version": "v1"
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