S.N. Petrova

One of the main problems considered in this article is research of the chain stability. It is established that the chain stability is a concept more strong than the concept of absolute stability and asymptotic stability ¬¬is a concept more strong than the chain stability. The definition of a chain of stability is based on the fundamental system of attracted neighborhoods. It is shown that the positively invariant compact is a chain-stable if and only if when it-s a pseudo-attracting set. This article describes an approach to studying the stability of non-compact trajectories. A theorem establishing a connection between the first extension and continuation of a filter is proved. In addition, the theorem establishing the criterion of stability in terms of neighborhoods of points belonging to the semi-trajectory is proved. The results can be applied to the qualitative study of nonlinear dynamic systems modeling various processes and phenomena.