Analysis of a remarkable singularity in a nonlinear DDE

作者：Davidow Matthew; Shayak B; Rand Richard H^*

来源：Nonlinear Dynamics, 2017, 90(1): 317-323.

DOI：10.1007/s11071-017-3663-2

• Delay-differential equation
• Harmonic balance
• Melnikov's integral

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.

• 出版日期2017-10