Theoretical and numerical modelling of chaotic electrostatic ion cyclotron (EIC) oscillations by Jerk equation

Abstract

In the last few years, third order explicit autonomous differential equations, known as jerk equations, have generated great interest as they show features of regular and chaotic motion. In this paper, we have modelled chaotic electrostatic ion cyclotron oscillations using a third order nonlinear ordinary differential equation (ODE) and investigated its nonlinear dynamical properties. The nonlinear ODE has been derived for a plasma system from a two fluid model in the presence of a source term, under the influence of an external magnetic field, which is perpendicular to the direction of the wave vector. It is seen that the equation does not require an external forcing term to obtain chaotic behaviour. The stability of the solutions of the equation has been investigated analytically as well as numerically, and the bifurcation diagram obtained shows a number of interesting phenomena for various regimes of parameters. The coexisting attractors as well as their corresponding basins are shown and the phase space portraits at different conditions are obtained numerically and shown here. The results obtained here are in agreement with preliminary experiments conducted for a similar configuration of a plasma system.