Spatial competition and repulsion: pattern formation and the role of movement

Abstract: This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and repulsion are both anti-crowding interactions, collective effects may lead to clusters of individuals, which can arrange periodically. Through the analysis of two models, it provides insights into the similarities and differences in the patterns formed and underlines the role of movement in shaping the spatial distribution of biological populations.