The models of point vortices motion in two-layer fluid and two-fluid plasma are considered. These two different physical models are described by the same system of equations for different values of a parameter β. Positive values of the parameter correspond to the geostrophic model of a two-layer fluid, and negative ones correspond to a two-fluid plasma.

The stability analysis of the stationary rotation of a system of N identical point vortices lying uniformly on a circle of radius R in one of layers is presented. The problem has three parameters: N, R and β. The stability of the stationary rotation is interpreted as orbital stability. The instability of the stationary rotation is instability of system reduced equilibrium. The quadratic part of the Hamiltonian and eigenvalues of the linearization matrix are studied.

The parameters space (N,R,β) is divided on three parts: the domain of stability in an exact nonlinear setting, the linear stability domain, where the stability problem requires the nonlinear analysis, and the instability domain.

For the two-layer quasigeostrophic model the stability is studied for any values N=2,3,...
The results are published in the paper ``L. Kurakin, I. Lysenko, I. Ostrovskaya, M. Sokolovskiy. On stability of the Thomson's vortex N-gon in the geostrophic model of the point vortices in two-layer fluid. Journal of Nonlinear Science. 2018. DOI 10.1007/s00332-018-9526-2''.

For two-fluid plasma the cases N=2,...,11 are considered. Part of the results included in the paper ``I. Lysenko. On stability of a vortex triangle, square and pentagon in the two-fluid plasma'' and accepted for publication in Scientific-Educational and Applied Journal University News. North-Caucasian Region. Natural Sciences Series.

The work of the first three authors was supported by the Ministry of Education and Science of the Russian Federation, Southern Federal University (Projects No. 1.5169.2017/8.9 and No. 14.W03.31.0006).