Parametric excitation and chaos through dust-charge fluctuation in a dusty plasma

TL;DR

This paper investigates how dust-charge fluctuations in dusty plasma can induce chaos and parametric resonance in a simplified mathematical model, revealing routes to chaos and phase locking phenomena.

Contribution

It introduces a detailed numerical analysis of a vdPM equation modeling dusty plasma, highlighting chaos routes and resonance behaviors due to dust-charge fluctuations.

Findings

Chaos via period doubling and bifurcation identified

Frequency locking at 2:1 parametric resonance observed

Dust-charge fluctuation induces complex dynamical regimes

Abstract

We consider a van der Pol-Mathieu (vdPM) equation with parametric forcing, which arises in a simplified model of dusty plasma with dust-charge fluctuation. We make a detailed numerical investigation and show that the system can be driven to chaos either through a period doubling cascade or though a subcritical pitchfork bifurcation over an wide range of parameter space. We also discuss the frequency entrainment or frequency-locked phase of the dust-charge fluctuation dynamics and show that the system exhibits 2:1 parametric resonance away from the chaotic regime.