Robust chaos in a totally symmetric network of four phase oscillators

We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged analogue of the Lorenz attractor. The attractors emerge near the triple instability threshold of the splay-phase synchronization state of the oscillators. We provide theoretical arguments and verify numerically, based on the pseudohyperbolicity test, that the chaotic dynamics are robust with respect to small, e.g. time-dependent, perturbations of the system. The robust chaoticity should also be inherited by any network of weakly interacting systems with such attractors.