Perestyuk Y. An investigation of the certain class of discontinuous dynamical systems

This thesis is concerned with establishment of the sufficient conditions for the linear and weakly nonlinear systems of differential equations on the plane, with impulsive perturbations when phase point crosses the lines set, establish necessary and sufficient conditions of the family explosive one- and two- impulse trajectories discontinuous periodic solutions, sufficient conditions for the existence of such isolated cycle, construction of asymptotic approximation to them. Proposed method for studying a wide class of nonlinear mechanical systems pendulum in an environment with a high resistance, which are subjected to an impulse perturbations. It is shown that due to the linear impulse perturbation even "damped pendulum" can be converted into swinging. Sufficient conditions for asymptotic stability and instability of solutions of a wide class of linear extensions of dynamical systems on the torus, and also investigated the existence of invariant toroidal set of discontinuous dynamical systems, phase space all others are direct product of m-dimensional torus Tm and n-dimensional euclidean space Rn, formulated sufficient conditions of asymptotic stability set.