A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

Ioannis Kourakis, M. Momeni, M. Moslehi-Fard, P.K. Shukla

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.
Original languageEnglish
Article numberF06
Pages (from-to)F473-F481
Number of pages9
JournalJournal of Physics A: Mathematical and Theoretical
Issue number24
Publication statusPublished - 15 Jun 2007

ASJC Scopus subject areas

  • Mathematical Physics
  • Modelling and Simulation
  • Statistics and Probability
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics


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