Volume 7, Number 3, Fall 1999
RESONANT CODIMENSION TWO BIFURCATION
IN THE HARMONIC OSCILLATOR
WITH DELAYED FORCING
SUE ANN CAMPBELL AND JACQUES BÉLAIR
Abstract. We study a delay differential equation modeling
the harmonic oscillator with forcing which depends on the
state and the derivative of the state at some time in the past.
We perform a linearized stability analysis of the equation and
describe the location of Hopf and steady state bifurcations in
the parameter space. A complete description of the location
of points in parameter space where the characteristic equation
possesses two pairs of pure imaginary roots, ±iω1, ±iω2 with
ω1 : ω2 = m : n, m, n ∈ Z+, is given.