Abstract
It is well known that some methods of qualitative analysis of nonlinear systems are based on reduction of the initial system of equations to one more suitable for the investigation. Moreover, the dimension of the reduced system may appear to be smaller (or larger) than that of the initial system. For example, the application of a vector Lyapunov function results in a quasimonotone comparison system of a smaller dimension [1]. On the other hand, the incorporation of the inclusion principle [4] or a matrix Lyapunov function [3] in the analysis of the dynamics of nonlinear (linear) systems yields an enlargement of the initial system.
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