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, ±iω_{1}, ±iω_{2} with
ω_{1} : ω_{2} = m : n, m, n ∈ Z^{+}, is given.
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