Chaotic Dynamics in Generalized Rabinovich System

Abstract

The article is devoted to the study of the global behavior of the generalized Rabinovich system describing the process of interaction between waves in plasma. For this generalized system, we obtain the positive invariant set (ultimate bound) and globally exponential attractive set using the approach where we transform the initial problem of finding the corresponding set to the conditional extremum problem and solve this problem. Furthermore, the rate of the trajectories going from the exterior of the attractive set to the interior of the attractive set is also obtained. Numerical localization of attractor is presented. Meanwhile, the volumes of the ultimate bound set and the global exponential attractive set are obtained, respectively. The main innovation of this article lays in considering the generalized form of the Rabinovich system with [Formula: see text] and obtaining the results on the ultimate bound set and globally exponential attractive set for this general case.