Analysis of a remarkable singularity in a nonlinear DDE

2017/01/01 by Davidow, Matthew, Shayak, B., Rand, Richard H. · 1 citation
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.1701.00201

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.

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