The objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point. A new technique of investigation is presented. Conditions for existence of the foci and centres are proposed. The focus-centre problem...

Our purpose is to obtain by using Lyapunov second method criteria for stability, asymptotical stability and instability of nontrivial solutions of the impulse systemwhere Δ|:= (+) − (), (+) = lim+ (). Construction of a reduced system in the neighbourhood of a nontrivial solution is a central...