A nonlinear system of finite-difference equations of a general form, which admits a partial (in part of variables) zero equilibrium position, is considered. An approach to studying the stability of this equilibrium position is described, based on a preliminary study of stability in a part of the variables determining it based on the Lyapunov function method, followed by an analysis of the structural form of the system. To expand the possibilities of this approach, it is proposed to correct the area in which the Lyapunov function is constructed; this is achieved by introducing a second (vector, generally speaking) auxiliary function. Examples are given that show the features of this approach.
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