Abstract:Background. The oscillating motions of dynamic systems are investigated, namely, motions that are not bounded and, in addition, have the property that they do not tend to infinity as time tends to plus infinity. Such motions play an important role in various problems of mathematical physics, celestial mechanics, thermodynamics and astrophysics. Materials and methods. New concepts related to the oscillation of the set of all solutions of a system of differential equations are introduced into consideration: the concept of equioscillation in the limit of the set of all solutions and partial analogues of this concept. Results. Based on the principle of comparison of Matrosov with Lyapunov vector functions and the connection found by the author between Poisson boundedness and oscillability of solutions, sufficient conditions for equioscillability in the limit of the set of all solutions, as well as partial analogues of these conditions, are obtained. The work continues the author's research on the study of the boundedness and oscillation of the sets of all solutions of differential systems using Lyapunov functions and Lyapunov vector functions. Conclusions. The obtained theoretical results can be used to analyze complex dynamic systems in various fields of science.
Fulltext:
PDF file (403 kB)