Samukham, S
(2015)
Homotopy Continuation for Characteristic Roots of Delay Differential Equation.
Masters thesis, Indian Institute of Technology Hyderabad.
Abstract
In this thesis we develop a homotopy continuation method to find the characteristic roots of scalar delay differential equations with multiple delays. We introduce a homotopy parameter µ € [0;1] in such a way that for µ  0, the characteristic equation contains only one delay term and for µ  1 the original characteristic equation is recovered. By selecting µ  0 allows us to express all the roots of the characteristic equation in closed form in terms of Lambert W function. A numerical continuation based scheme is then developed to trace the roots as µ is varied from 0 to 1. The roots of the characteristic equation for µ  1 correspond to the characteristic roots of the delay differential equation. We show several numerical examples to demonstrate the developed method.
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