Interplay between local and global order controls bifurcations in nonreciprocal systems without a conservation law

We elucidate the generic bifurcation behavior of local and global order in short-range interacting nonreciprocal lattice systems without conservation laws. We show that a critical magnitude of nearest-neighbor correlations within the respective lattices controls the emergence of coherent oscillations of global order as a result of frustration. Local order is maintained during these oscillations, implying non-trivial spatio-temporal correlations. Ghost states emerge in the strong-interaction regime. The residence time in either of these states eventually diverges, giving rise to ordered non-equilibrium steady states via a saddle-node-infinite-period bifurcation. Our work provides a comprehensive microscopic understanding of collective phenomena in nonreciprocal matter without conservation laws, which may be relevant e.g. for understanding enzyme clustering.