Self-excitation, Parametric Forcing, and Chaos in the Dynamics of Dust-Grain Charge in Dusty Plasmas

Abstract

The Van der Pol equation describing self-excited oscillations, and the Mathieu equation exhibiting parametric excitation, are each well-studied and have numerous applications in physics, engineering, and biology. A combined Van der Pol-Mathieu equation has been shown to arise from a simple model for the dynamical behavior of charged dust grains in dusty plasmas (Momeni et al., 2005). A systematic numerical study of this combined equation reveals a rich variety of nonlinear behavior including widespread chaos. An improved derivation of the equation leading to quasiperiodic parametric forcing, as well as the inclusion of external forcing and Duffing nonlinearity have also been studied.