Title: Analysis of a remarkable singularity in a nonlinear DDE,
Abstract: In this work we investigate the dynamics of the nonlinear DDE
(delay-differential equation)
x''(t)+x(t-T)+x(t)^3=0
where T is the delay. For T=0 this system is conservative and exhibits no
limit cycles. For T>0, no matter how small, an infinite number of limit cycles
exist, their amplitudes going to infinity in the limit as T approaches zero.
We investigate this situation in three ways: 1) Harmonic Balance, 2)
Melnikov's integral, and 3) Adding damping to regularize the singularity.