  The interplay between activity and elasticity often found in active and
living systems triggers a plethora of autonomous behaviors ranging from
self-assembly and collective motion to actuation. Amongst these, spontaneous
self-oscillations of mechanical structures is perhaps the simplest and most
wide-spread type of non-equilibrium phenomenon. Yet, we lack experimental model
systems to investigate the various dynamical phenomena that may appear. Here,
we report self-oscillation and synchronization transitions in a
centimeter-sized model system for one-dimensional elasto-active structures. By
combining precision-desktop experiments of elastically coupled self-propelled
particles with numerical simulations and analytical perturbative theory, we
demonstrate that the dynamics of single chain follows a Hopf bifurcation. We
show that this instability is controlled by a single non-dimensional
elasto-active number that quantifies the interplay between activity and
elasticity. Finally, we demonstrate that pairs of coupled elasto-active chains
can undergo a synchronization transition: the oscillations phases of both
chains lock when the coupling link is sufficiently stiff. Beyond the canonical
case considered here, we anticipate our work to open avenues for the
understanding and design of the self-organisation and response of active
artificial and biological solids, e.g. in higher dimensions and for more
intricate geometries.
