Swarmalators

Oscillators that synchronize AND swarm — five collective phases

J (spatial): 0.10 K (phase): 1.00 N agents: 60

Swarmalators (Lee, Bain, Perez-Cervantes 2021) are oscillators with coupled spatial and phase dynamics: ẋᵢ = vᵢ + J Σ F(xⱼ−xᵢ)cos(θⱼ−θᵢ), θ̇ᵢ = ωᵢ + K Σ G(xⱼ−xᵢ)sin(θⱼ−θᵢ). Five phases emerge: async (K≈0), static-async, static-sync (K large +), static-wave, and splintered-phase states.