Localization of the attractors of the non-autonomous Liénard equation by the method of discontinuous comparison systems
Consider the non-autonomous Liénard equation \[ dy/dt=-\mu(F(y)- E(t))- x,\quad dx/dt=y,\tag{\(*\)} \] where \(F\) and \(E\) are Lipschitzian, \(\mu\) is a positive parameter. By means of discontinuous comparison systems of dry friction type, the author constructs a simply connected region containing the global attractor of \((*)\), provided the right-hand side of \((*)\) satisfies certain conditions, which are quite common for Liénard systems. As an application, an autonomous system of van der Pol's type is considered.
scientific article; zbMATH DE number 1042192