Stable Oscillation and Chaotic Motion of the Dust-Acoustic Waves for the KdV–Burgers Equation in a Four-Component Dusty Plasma

Abstract

Investigation of nonlinear dust-acoustic waves (DAWs) in a four-component unmagnetized electron–ion dusty plasma composed of fluid dust species, the Maxwellian positive, and negative ions with $q$ -nonextensive electrons is performed. The dust charge variation is considered for both adiabatic and nonadiabatic cases. For the nonadiabatic case, the Korteweg-de Vries–Burgers (KdV-B) equation is obtained utilizing the reductive perturbation technique (RPT). Implementing the traveling wave transfiguration, the KdV-B equation is transformed into a planar dynamical system (PDS). Implementing the phase plane theory of PDS, qualitative phase portrait profiles of a stable spiral for the corresponding system are presented. The effects of relevant physical parameters are shown on the DAW behavior. Dynamical features, such as quasiperiodic and chaotic motions of the system, are presented via a numerical investigation in the presence of an extraneous periodic force. Sensitivity analysis and the box-counting dimensions for chaotic profiles are presented.