Swarmalators

Examples of several states of the swarmalator phase diagram, see Fig. 6.11.
The video has two time scales t∈[0,150] and t∈[150,1000].

Classes of steady states of N=100 swarmalators after a duration of t=1000. The top row shows the steady states in 2D position space where the color corresponds to ϕ_j - Ψ, i.e., the phase of each swarmalator subtracted by the complex phase of the order parameter W defined in Eq. (6.6.3). The order parameter R is the Kuramoto model order parameter defined in Eq. (6.1.3). The second row shows the correlation between the phase ϕ_j - Ψ of the swarmalators and their azimuthal angle φ_j. (a) Static Asynch (StA) for (K,J)=(-0.8,0.2). (b) Active Phase Wave (ActPW) for (K,J)=(-0.8,1). (c) Splintered Phase Wave (SpPW) for (K,J)=(-0.1,1). (d) Static Phase Wave (StPW) for (K,J)=(0,1). (e) Static Synch (StS) for (K,J)=(0.1,0.2). For small |W|, Ψ is fluctuating and leads to the fluctuation of the color even if ϕ_j is stable.