Effect of Nonreciprocal Forces on the Stability of Dust Clusters

Results are presented from studies of the stability of the plane dust clusters in the form of a regular polygon with the number of particles from two to five. It is assumed that the particles are placed in the plasma consisting of Maxwellian electrons and a directed flow of cold ions. It is shown that, in such clusters, the oscillatory instabilities can develop along with the aperiodic instabilities. The ranges of plasma parameters are determined, within which the oscillatory instability of the five-particle cluster becomes saturated at the weakly nonlinear stage. As a result, the cluster forms a time crystal, which can be a chiral crystal.