Self-organizing states of swarmalator collectives with phase lag

We investigate the effect of phase lag on the two-dimensional swarmalator collectives. We find that the parameter space of dynamical states with spatial angle and phase correlation, and kinetic energy increases with increase in the phase lag of the swarmalators by decrease the spread of the static asynchronized state without any space-phase correlation and kinetic energy. The phase lag parameter also induces cluster states and breathing chimera for the attractive phase coupling among the swarmalators. The phase lag parameter manifests abrupt transitions in the order parameters characterizing the dynamical states and facilitates extreme multistability among the observed dynamical states of the swarmalator collectives. We deduce the analytical stability condition for the static synchronized state for a system of two coupled swarmalators, which agrees with the simulation results of an ensemble of swarmalator collectives with phase lag.