Synchronization is a universal phenomenon observed in systems like coupled lasers and heart cells, where units align
rhythms but remain stationary. Swarming, seen in bird flocks and fish schools, is a related effect where units coordinate
spatial movements without synchronizing internal oscillations. Some systems coordinate in both space and time, such as
Japanese tree frogs synchronizing calls while grouping, or starfish embryos syncing genetic cycles with movements to form
"living crystals". Driven colloids like Janus particles and Quincke rollers also exhibit this dual behavior.

Theoretical studies on systems mixing sync and swarming, such as swarmalators, are growing but remain challenging due to
their nonlinearities and complexity. Active matter models, like the Vicsek model, require advanced statistical physics
methods and are often only partially solved numerically. Fully analyzable active matter models are rare.

In this talk, I present a model of non-identical swarmalators, combining synchronization and swarming, which exhibits four
collective states: asynchrony, sync clusters, vortex-like phase-waves, and a mixed state. These states mirror behaviors in
biological microswimmers, chemical nanomotors, and drones. Using a generalized Ott-Antonsen ansatz, we provide the first
analytic description of these states, offering insights into active matter and related fields.