‘Butterfly chaos effect’ discovered in swarms and herds of animals
Center of mass trajectories of different attractors for N=128, R0=v0=1, η=0 and different β. (a) Period 2 (β=60000) and period 4 (β=300) attractors. (b) Quasiperiodic attractor that appears at β=2N=256. (c) Periodic solutions with larger periods: 6 (β=N=128), 5 (β≈177), and 13 (β≈225). (d, e) Torus-like chaotic attractor for β=1 depicted for a long and a shorter time interval. (f) Chaotic attractor for β=0.01 : the center-of-mass trajectory will fill a…