Spontaneous excitation of limit cycles in living chiral crystals

Broken parity and time reversal symmetries lead to the emergence of nonreciprocal interactions in chiral active matter. In a recent study, we observed a remarkable consequence of such emergent nonreciprocity in the form of spontaneous long-lived strain oscillations in living chiral crystals (LCCs) of starfish embryos (Tan*, Mietke* et al., Nature, 607, 287-293, 2022). Here, we combine insights from new experiments and data analyses to show that these long-lived oscillations correspond to limit cycles in strain space. The spontaneous excitation and eventual decay of strain oscillations results from the system switching stochastically between two attractors: a stable limit cycle, and a stable fixed point corresponding to the static ground state of the LCC. Our experimental observations are well-captured qualitatively by a minimal phenomenological nonlinear model comprising of nonreciprocal couplings between two strain fields and a global order parameter. The bistability between static and oscillatory states implies that oscillations can be induced using external perturbations in a controlled manner. Our results show that LCCs serve as paradigmatic active metamaterials in which nonreciprocity and nonlinearity combine to facilitate selective actuation of work generating limit cycles.