Abstract:
In this paper we study oscillating motions of dynamic systems, 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. In this paper we introduce new concepts related to the oscillability of the set of all solutions of a system of differential equations, namely, the concept of equioscillability of the set of all solutions and partial analogues of this concept. Based on the principle of comparison of Matrosov with Lyapunov vector functions and the connection between Poisson boundedness and oscillability of solutions found by the author, sufficient conditions for the equioscillability of the set of all solutions are obtained, as well as partial analogues of these conditions. The paper continues the author's research on the study of boundedness and oscillability of sets of all solutions of differential systems using Lyapunov functions and Lyapunov vector functions. The obtained theoretical results can be used for the analysis of complex dynamic systems in various fields of science.
Keywords:poisson equiboundedness of solutions, equioscillation of solutions, lyapunov vector function.
