State: —
Swarmalators (Lee, Hannay, Ott 2020): N particles with position xᵢ∈ℝ² and phase θᵢ∈[0,2π).
ẋᵢ = Σⱼ [(xⱼ−xᵢ)/|xⱼ−xᵢ| · (1 + J cos(θⱼ−θᵢ)) − (xⱼ−xᵢ)/|xⱼ−xᵢ|³]
θ̇ᵢ = ω + K Σⱼ sin(θⱼ−θᵢ)/|xⱼ−xᵢ|
Color encodes phase θ. Five collective states: static sync (J>0,K large), static async (K negative), phase wave (ring with phase gradient), active wave, active phase wave.
ẋᵢ = Σⱼ [(xⱼ−xᵢ)/|xⱼ−xᵢ| · (1 + J cos(θⱼ−θᵢ)) − (xⱼ−xᵢ)/|xⱼ−xᵢ|³]
θ̇ᵢ = ω + K Σⱼ sin(θⱼ−θᵢ)/|xⱼ−xᵢ|
Color encodes phase θ. Five collective states: static sync (J>0,K large), static async (K negative), phase wave (ring with phase gradient), active wave, active phase wave.