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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.06291 |
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| _version_ | 1866912814283620352 |
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| author | Rossatto, R. G. Alvarez, H. Ariel Carlevaro, C. Manuel Bordin, José Rafael |
| author_facet | Rossatto, R. G. Alvarez, H. Ariel Carlevaro, C. Manuel Bordin, José Rafael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06291 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Confinement-controlled chase-escape dynamics Rossatto, R. G. Alvarez, H. Ariel Carlevaro, C. Manuel Bordin, José Rafael Statistical Mechanics Applied Physics 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. |
| title | Confinement-controlled chase-escape dynamics |
| topic | Statistical Mechanics Applied Physics |
| url | https://arxiv.org/abs/2601.06291 |