Continuation Methods As the Link between Perturbation Analysis and Asymptotic Analysis

Abstract

We shall study the periodic orbits of the Rayleigh oscillator which depend on the damping parameter, denoted by c. For small values off c we use perturbation analysis to examine periodic orbits. For large values of c we use asymptotic analysis. For intermediate values of c we describe a computational technique which we denote by “continuation method” to determine the periodic orbits. The periodic orbits found in this way approach the perturbed and the asymptotic solutions as c becomes small and large, respectively. Because of this the intermediate solution is referred to as a link.