  Non-reciprocal systems exhibit diverse dynamical phases whose character
depends on the type and degree of non-reciprocity. In this study, we
theoretically investigate dynamical structures in a mixture of non-reciprocally
aligning polar active particles with repulsion, focusing on the performance on
(and connection between) different levels of description. Linear stability
analyses of the associated continuum model predict a profound influence of
non-reciprocity, leading to phase separation, (anti-)flocking and asymmetric
clustering behavior. On the microscopic level, particle simulations confirm the
emergence of these dynamical phases and allow for a more in-depth investigation
of (microscopic) properties, including orientational correlations and
susceptibilities. The drastic impact of orientational couplings alone on the
density dynamics is demonstrated in particle simulations without repulsion,
where non-reciprocal alignment leads to the asymmetric formation of
single-species polarized clumps. Overall, our findings demonstrate that certain
dynamical properties, like a chase-and-run behavior in the asymmetrical
clustering phase, are overlooked in mean-field continuum theory, making
microscopic simulations an indispensable tool for studying the effects of
non-reciprocal alignment couplings.
