We investigate the dynamics of the nonlinearwhere 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.
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