Abstract
The particle dynamics in the photogravitational field of a binary star is considered in the framework of the limited three-body problem with two radiating masses. A nonlinear computer simulation of the stability of triangular libration points is carried out. In the configuration space and in the space of system parameters, regions of stable clusters of particles of gas-dust formations are constructed with the identification of the resonant set of points of the 3rd and 4th orders. It is shown that in the absence of a third-order resonance in the stability region of the linear system, Lyapunov stability everywhere takes place. At a fourth-order resonance, Lyapunov stability is preserved with the exception of many points (depending on the value of the mass parameter) at which stability can be violated.