Pattern Formation in Populations with Density-Dependent Movement and Two Interaction Scales
Fig 2
Spatial distribution of the population from the particle-level model.
Spatial distribution at long times of a population of 104 individuals using the dynamics of Eq (1) with a short interaction range Rs = 0.05 and a long interaction length Rl = 0.1. D0 = 10−4, a = 1 in all the panels. Every individual is plotted as a small black dot. The system is a square area of lateral size L = 1 with periodic boundary conditions. Upper panel: b = 3.5 × 10−4, c = 7.0 × 10−4 (homogeneous distribution). Left bottom panel: b = 8.5 × 10−4, c = 7 × 10−4 (labyrinth pattern). Right bottom panel: b = 4.3 × 10−4, c = 3.9 × 10−4 (spot pattern). Note the rings with higher density in the border.