Bifurcations in Delay Differential Equations: an algorithmic approach in frequency domain

TL;DR

This paper introduces an algorithmic frequency domain approach to analyze bifurcations and local oscillations in delay differential equations, providing a systematic way to find periodic solutions.

Contribution

It develops an iterative method to derive bifurcation equations for delay differential equations, enabling symbolic computation of local periodic solutions.

Findings

Bifurcation equations can be systematically derived using the proposed method.

The iterative approach allows arbitrary order approximation of bifurcation equations.

Implementation in symbolic math programs facilitates practical analysis.

Abstract

In this work we study local oscillations in delay differential equations with a frequency domain methodology. The main result is a bifurcation equation from which the existence and expressions of local periodic solutions can be determined. We present an iterative method to obtain the bifurcation equation up to a fixed arbitrary order. It is shown how this method can be implemented in symbolic math programs.