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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, nZ+, is given.

 

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