Global attraction to the origin in a parametrically driven nonlinear oscillator

We consider a parametrically-driven nonlinear ODE, which encompasses a simple model of an electronic circuit known as a parametric amplifier, whose linearisation has a zero eigenvalue. By adopting two different approaches, we obtain conditions for the origin to be a global attractor which is approached (a) non-monotonically and (b) monotonically. In case (b), we obtain an asymptotic expression for the convergence to the origin. Some further numerical results are reported.

• Type: Journal
• Year: 2004
• Where: AMC
• Authors: M. V. Bartuccelli, J. H. B. Deane, G. Gentile, S. A. Gourley
• Keywords: AMC 2004, Parametric Amplifier, Parametrically-driven Nonlinear Ode, Simple Model