Numerical Solutions of Van Der Pol-Mathieu Type Nonlinear Ordinary Differential Equation in Complex Plasma

Abstract

The description dust plasma behavior via a multi-fluid model, Where it represents that Boltzmann distributed electrons and ions, the dust momentum and Poisson's equations, in addition to the continuity equation that has a source term for the dust grains. The Runge-Kutta technique of fourth order was then used to numerically solve the equation. The solution shows a variety of behaviors under wide range of parameters changes. In particular, the solution of the equation shows a chaotic behavior  at  α= 1.0. In this study, the chaotic behavior in the plasma complex is graphically studied and discussed for some certain parameters. The aim of this study can be helped the researchers to investigate several nonlinear oscillations in different plasma and fluid mechanics models.