The results of the numerical investigation of a layered structure formation in systems of particles with anisotropic pair interaction are presented. A simulation was carried out for extended homogeneous structures consisting of one or several layers of interacting particles over a wide range of parameters which correspond to the conditions usually observed in laboratory dusty plasma experiments. For the first time a detailed analysis of the development of various instabilities in such systems has been undertaken.

Generalized analytical equations for the mean kinetic energy, mean-square displacement and noise-averaged trajectory of a self-propelled particle with both translational and rotational inertia and velocity fluctuations are proposed.

Simple corrections are proposed to the basic theory of overdamped active Brownian motion, which allow one to calculate the effective diffusion coefficient and the persistence length of a self-propelled particle in a medium with any dynamic viscosity.

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