Analysis of a van der Pol Type Differential Equation Having a Nonpolynomial Elastic Term

Ronald Mickens Clark Atlanta University

The standard van der Pol differential equation provides a model for many important phenomena in the natural and engineering sciences. For this equation the force function is a linear function of the dependent variable; consequently, in the absence of nonlinear terms, the ODE reduces to a damped harmonic oscillator. We consider a modification for which the force function contains terms that are odd, but nonpolynomial in the dependent variable. We use a variety of techniques (energy arguments, phase-space methods, and perturbation procedures) to study the asymptotic behavior of solutions to these van der Pol type ODE’s.

The work reported here was supported in part by research grants from DOE and the MBRS-SCORE Program at Clark Atlanta University.