The period of relaxation oscillations of a nonlinear system using singular perturbation methods

Abstract

We determine the period of relaxation oscillations of a physical system governed by the nonlinear Liénard equation ε xⁿ + (ax² - b) x\' + x +cx³ = 0 where a, b, c > 0, 0 < ε << 1, using singular perturbation methods. These methods which involve considering matched asymptotic expressions of different layers yield a uniformly valid expansion for the above equation and hence the relaxation oscillations. The van der Pol equation is a special case of the above equation.

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 211-222