Data-driven exploration of swarmalators with second-order harmonics.

We explore the dynamics of a swarmalator population comprising second-order harmonics in phase interaction. A key observation in our study is the emergence of the active asynchronous state in swarmalators with second-order harmonics, mirroring findings in the one-dimensional analog of the model, accompanied by the formation of clustered states. Particularly, we observe a transition from the static asynchronous state to the active phase wave state via the active asynchronous state.