Dynamical Systems Seminar

Richard RandCornell University
A remarkable singularity in a delay-differential equation
Monday, September 11, 2017 - 3:30pm
Malott 224

Based on a paper coauthored with grad students Matt Davidow and B. Shayak.

The differential equation $x'' + x + x^3 =0$ is conservative and admits no limit cycles. If the linear term $x(t)$ is replaced by a delayed term $x(t-T)$, where $T$ is the delay, the resulting delay-differential equation exhibits an infinite number of limit cycles for positive values of $T$ in the neighborhood of $T=0$, their amplitudes going to infinity in the limit as $T$ approaches zero.

This bifurcation will be illustrated through the use of a variety of tools from nonlinear dynamics: harmonic balance, Melnikov's integral and numerical integration.