### The stability of solutions for a non-linear system of finite-difference equations with respect to part of the variables

Title The stability of solutions for a non-linear system of finite-difference equations with respect to part of the variables E. V. Afinogentova11National Research Ogarev Mordovia State University In this paper we use the method of the auxiliary ($\mu$-system \cite{afevBiben1}) for solving the stability problem with respect to some variables for nonlinear systems of finite-difference equations. The advantage of the method is that the question of stability with respect to some variables reduces to solving the stability problem for all variables. The method is based on the construction of special \ mu-systems, depending on their stability or instability, make a conclusion about the stability with respect to given variables of the zero solution of the original system. For a linear discrete system the realization of this method was proposed in \cite{afevBiben2}, \cite{afevBiben3}. finite-difference equations, stability with respect to some variables, Lyapunov function Afinogentova E. V. ''The stability of solutions for a non-linear system of finite-difference equations with respect to part of the variables'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 353-359. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper49.pdf. - Date of access: 12.04.2021.