Swarmalators with thermal noise

We investigate a population of swarmalators, mobile versions phase oscillators that both sync in time and swarm through space. focus on an $XY$-type model identical swarmalators running one-dimensional ring subject to thermal noise. uncover four distinct collective states, some which capture the behavior real-world such as vinegar eels sperm. Among these, most intriguing is ``mixed state,'' blends two other states. present comprehensive diagram from Fourier mode analysis with high accuracy, excellent agreement numerical simulation results. Our serves tractable toy for systems self-synchronize self-assemble interdependently.