2018/07/22 by Si Tang, Tang, Si, George Kordzakhia +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Biological sciences #FOS: Physical sciences #Populations and Evolution (q-bio.PE) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1807.08387
6 pages
arxiv created 2018/07/22 · openalex publication_date 2018/07/22 · arxiv updated 2018/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Chase-Escape is a simple stochastic model that describes a predator-prey interaction. In this model, there are two types of particles, red and blue. Red particles colonize adjacent empty sites at an exponential rate λR, whereas blue particles take over adjacent red sites at exponential rate λB, but can never colonize empty sites directly. Numerical simulations suggest that there is a critical value pc for the relative growth rate p:=λR/λB. When p<pc, mutual survival of both types of particles has zero probability, and when p>pc mutual survival occurs with positive probability. In particular, pc ≈ 0.50 for the square lattice case (\mathbb Z2). Our simulations provide a plausible explanation for the critical value. Near the critical value, the set of occupied sites exhibits a fractal nature, and the hole sizes approximately follow a power-law distribution.