Study of Dynamic System with Impulse Action

Nonlinear dynamic systems with chaotic regimes have found wide application in various fields. The issue of controlling complex processes by means of an external pulse signal is one of the fundamental tasks. The possibility of controlling external instantaneous effects in order to stabilize the chaotic regimes of the system [1], [2] expands the practical application of complex systems.Nonlinear dynamic systems with chaotic regimes have found wide application in various fields. The issue of controlling complex processes by means of an external pulse signal is one of the fundamental tasks. The possibility of controlling external instantaneous effects in order to stabilize the chaotic regimes of the system [1], [2] expands the practical application of complex systems.In this paper, we consider dynamic processes with discontinuous trajectories and generalized impulse-type controls. The considered system with localized singularities is transformed into a boundary value problem without singular terms. The presence of instantaneous effects on the system is observed in the boundary conditions. To solve the resulting problem, classical methods can be used.