Fractal representation of electron-acoustic waves in the Earth’s auroral zone

Abstract

Nonlinear small-amplitude electron-acoustic wave features and their fractal representations are explored in the Earth’s auroral zone plasma having cold fluid electrons, hot (r,q)-distributed electrons, and stationary ions. The dynamics of the phase space is investigated through the formulation of the Laedke-Spatschek (LS) equation by the method of reductive perturbation. The computational simulation reveals that when a system experiences a periodic driving force then the oscillation of electrostatic potential shows a transition from quasiperiodic to chaos. The reconstruction of a dynamical system is performed using the fractal interpolation function with the appropriate choice of scaling factor to measure the irregularity of the system in terms of fractal dimension, which enlightens the system’s self-similar nature. The existence of chaotic features is quantified with the Lyapunov exponents. With an increase in electron temperature, fractal dimension is predicted to decrease, indicating a greater complexity and irregularities in the system. The type of analysis used for this work is particularly useful when the dynamical system exhibits irregularities in phase profiles.