The purpose the purpose of this study is to mathematically describe an ensemble of oscillators coupled by a common dipole field, to model and study the synchronization of the three topologies under consideration: a ring, a grid, and a special case of a lattice-chain, with subsequent identification of a priority topology that would ensure synchronization over a larger range of initial conditions of the ensemble.

Methods. To simplify the numerical modeling and study the synchronization of systems of antiferromagnetic oscillators coupled by a common dipole field, the Kuramoto model for coupled oscillators, as well as the order parameter and its average value, were used.

Results. A mathematical model for antiferromagnetic oscillators coupled by a common dipole field was obtained for three topologies: ring, grid, and chain. Using the Kuramoto model of coupled oscillators and the order parameter and its average value, the synchronization of the considered arrays was studied, and it was found that the lattice is the preferred topology for the same ensemble parameters.

Conclusion. The paper studies the problem of synchronization of ensembles of antiferromagnetic spin-Hall oscillators (AFM SCHO) combined into different topologies: ring, grid and chain. It is shown that the grid is the most preferable topology for achieving synchronization at lower values of the coupling strength constant between the moscillators. The ring and chain require higher values of the coupling strength constant, which is their disadvantage. Nevertheless, with a sufficiently strong coupling, synchronization is also possible in these topologies.