Homotopy continuation for characteristic roots of delay differential equations using the Lambert W function

Surya, S and Vyasarayani, C P and Kalmár-Nagy, T (2017) Homotopy continuation for characteristic roots of delay differential equations using the Lambert W function. Journal of Vibration and Control. p. 107754631771762. ISSN 1077-5463 (In Press)

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Abstract

In this work, we develop a homotopy continuation method to find the characteristic roots of delay differential equations with multiple delays. We introduce a homotopy parameter μ into the characteristic equation in such a way that for μ = 0 this equation contains only one exponential term (corresponding to the largest delay) and for μ = 1 the original characteristic equation is recovered. For μ = 0, all the characteristic roots can be expressed in terms of the Lambert W function. Pseudo-arclength continuation is then used to trace the roots as a function of μ. We demonstrate the method on several test cases. Cases where it may fail are also discussed.

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