Localization of the attractors of the non-autonomous Liénard equation by the method of discontinuous comparison systems

Abstract The construction of simple discontinuous comparison systems with non-linear elements of the “dry friction” type is proposed. The sets of closed trajectories of such systems, which are contact-free with respect to the vector field of the initial system, enable one to obtain estimates off the dissipation domain simply. A similar approach is also used to construct annular domains. The absence of the property of convergence in the case of a Lienard system with a periodic additive term follows from the existence of these domains.