2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135598We 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.10 pages, 16 figuresChaotic DynamicsPlasma Physicstext