A qualitative investigation of coupled systems of nonlinear oscillators

Date

1985

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

This dissertation describes some qualitative properties of coupled systems of two nonlinear oscillators with symmetric linear diagonal couplings. Our particular interest is in the stability of in-phase periodic solutions and their dependence on the coupling coefficients. In this parameter space, the boundary of the stability region is characterized. We call it the critical surface. The types of bifurcation points and the asymptotes of the critical curve are established when the uncoupled system is 2-dimensional. In passing, a perturbation theorem for linear periodic systems is obtained. To illustrate the theory, we apply the results to coupled sinusoidal ocillators.

Description

Keywords

Differential equations, Asymptotic theory, Perturbation (Mathematics)

Citation