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Perturbations and Hopf bifurcation of the planar discontinuous dynamical system

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 and Hopf bifurcation are considered. Appropriate examples are given to ilustrate the bifurcation theorem.