Dynamics of delay systems with rapidly oscillating coefficients
The present paper considers the generalization of the averaging principle to delay systems and contains the following results described in the section ``conclusion'' of the paper: 1. It is shown that the averaged equation in delay systems can be rather complicated. In particular, the averaging can take the equation from the class of equations with lumped delay to the class of equations with distributed delay. 2. An algorithm is developed for studying the stability in nearly critical cases. It is shown that the phenomenon of unbounded process of alternation between stability and instability as the frequency of oscillations increases is typical of delay equations. 3. It is shown that the variations in the parameters (with zero mean) can significantly increase the stability domain. 4. It is shown that the phenomena of unbounded process of ``creation'' and ``termination'' of steady-state modes can arise in the nonlinear case.
scientific article; zbMATH DE number 6899059
scientific article