  We reveal that the mechanical pulsation of locally synchronised particles is
a generic route to propagate deformation waves. We consider a model of dense
repulsive particles whose activity drives periodic change in size of each
individual. The dynamics is inspired by biological tissues where cells consume
fuel to sustain active deformation. We show that the competition between
repulsion and synchronisation triggers an instability which promotes a wealth
of dynamical patterns, ranging from spiral waves to defect turbulence. We
identify the mechanisms underlying the emergence of patterns, and characterize
the corresponding transitions. By coarse-graining the dynamics, we propose a
hydrodynamic description of an assembly of pulsating particles, and discuss an
analogy with reaction-diffusion systems.
