  The presence and significance of active topological defects is increasingly
realised in diverse biological and biomimetic systems. We introduce a continuum
model of polar active matter, based on conservation laws and symmetry
arguments, that recapitulates both polar and apolar (nematic) features of
topological defects in active turbulence. Using numerical simulations of the
continuum model, we demonstrate the emergence of both half- and full-integer
topological defects in polar active matter. Interestingly, we find that
crossover from active turbulence with half- to full-integer defects can emerge
with the coexistence region characterized by both defect types. These results
put forward a minimal, generic framework for studying topological defect
patterns in active matter which is capable of explaining the emergence of
half-integer defects in polar systems such as bacteria and cell monolayers, as
well as predicting the emergence of coexisting defect states in active matter.
