Article: Davidow, M; Shayak, B; Rand, R; “Analysis of a Remarkable Singularity in a Nonlinear DDE”, Nonlinear Dynamics, 90 (1):317-323
Abstract: We investigate the dynamics of the nonlinear DDE (delay-differential equation) d(2)x/dt(2) (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 T is, 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.