Diffusive oscillators capture the pulsating states of deformable particles

We study a model of diffusive oscillators whose internal states are subject to a periodic drive. These models are inspired by the dynamics of deformable particles with pulsating sizes, where repulsion leads to arrest the internal pulsation at high density. We reveal that, despite the absence of any repulsion between the diffusive oscillators, our model still captures the emergence of dynamical arrest. We demonstrate that arrest here stems from the discrete nature of internal states which enforces an effective energy landscape analogous to that of deformable particles. Moreover, we show that the competition between arrest and synchronisation promotes spiral waves reminiscent of the pulsating states of deformable particles. Using analytical coarse-graining, we derive and compare the collective dynamics of diffusive oscillators with that of deformable particles. This comparison leads to rationalize the emergence of spirals in terms of a rotational invariance at the coarse-grained level, and to elucidate the role of hydrodynamic fluctuations.