An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Bifurcations, Center Manifolds, and Periodic Solutions
Published
Author(s)
David E. Gilsinn
Abstract
Nonlinear time delay differential equations are well known to have arisen in models in physiology, biology, and population dynamics. They have also arisen in models of metal cutting processes. Machine tool chatter, from a process called regenerative chatter, has been identified as self-sustained oscillations for nonlinear delay differential equations. The actual chatter occurs when the machine tool shifts from a stable fixed point to a limit cycle and has been identified as a Hopf bifurcation. This chapter develops the computational tools to determine whether a time-delay system satisfies the Hopf criteria and demonstrates the application of these tools on a model of a machine turning process.
Citation
Book chapter in Delay Differential Equations: Recent Advance
Gilsinn, D.
(2009),
Bifurcations, Center Manifolds, and Periodic Solutions, Book chapter in Delay Differential Equations: Recent Advance, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=51255
(Accessed April 25, 2024)