  Symmetries naturally occur in real-world networks and can significantly
influence the observed dynamics. For instance, many synchronization patterns
result from the underlying network symmetries, and high symmetries are known to
increase the stability of synchronization. Yet, here we find that general
macroscopic features of network solutions such as regularity can be induced by
breaking their symmetry of interactions. We demonstrate this effect in an
ecological multilayer network where the topological asymmetries occur
naturally. These asymmetries rescue the system from chaotic oscillations by
establishing stable periodic orbits and equilibria. We call this phenomenon
asymmetry-induced order and uncover its mechanism by analyzing both
analytically and numerically the suppression of dynamics on the system's
synchronization manifold. Moreover, the bifurcation scenario describing the
route from chaos to order is also disclosed. We demonstrate that this result
also holds for generic node dynamics by analyzing coupled paradigmatic
R\"ossler and Lorenz systems.
