Bifurcation analysis in a 3D symmetric system of interest in fusion plasma physics

Abstract

In this paper we study the pitchfork and Hopf bifurcations in a 3D dynamical system that models some oscillations of plasma parameters in Tokamaks. The pitchfork bifurcation's parameter is the input power in the system and the Hopf bifurcation is analyzed with respect of the three parameters of the system. In each case necessary and sufficient conditions for the occurrence of the Hopf bifurcation are provided. A special attention is paid to the case when the input power is varied. A case study is performed. It is emphasized the stable periodic orbits collision occurred after Hopf bifurcation, and the appearance of the double-scroll attractor.
It is also noticeable the coexistence of three attractors (two stable points and a double-scroll attractor) whose basins of attraction are analyzed.