Emergent nonreciprocal interactions violating Newton's third law are widespread in out-of-equilibrium systems. Phase separating mixtures with such interactions exhibit traveling states with no equilibrium counterpart. Using extensive Brownian dynamics simulations, we investigate the existence and stability of such traveling states in a generic nonreciprocal particle system. By varying a broad range of parameters including aggregate state of mixture components, diffusivity, degree of nonreciprocity, effective spatial dimension and density, we determine that traveling states do exist below the predator-prey regime, but nonetheless are only found in a narrow region of the parameter space. Our work also sheds light on the physical mechanisms for the disappearance of traveling states when relevant parameters are being varied, and has implications for a range of nonequilibrium systems including nonreciprocal phase separating mixtures, nonequilibrium pattern formation and predator-prey models.

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• Exotic phases of matter
• Nonequilibrium statistical mechanics
• Order parameters
• Phase diagrams