Estimation of the domain containing all compact invariant sets of a system modelling the amplitude of a plasma instability

In this Letter we describe localization results of all compact invariant sets of a system modelling the amplitude of a plasma instability proposed by Pikovski, Rabinovich and Trakhtengerts. We derive ellipsoidal and polytopic localization sets for a number of domains in the 4-dimensional parametrical space of this system. Other localization sets have been obtained by using paraboloids of a revolution, a circular cylinder and an elliptic paraboloid. Our approach is based on the solution of the first order extremum problem. A comparison of our method with the method of semipermeable surfaces is presented as well.