Characteristic roots for two-lag linear delay differential equations

David M.  Bortz

doi:10.3934/dcdsb.2016053

Article Contents

2016, Volume 21, Issue 8: 2409-2422. Doi: 10.3934/dcdsb.2016053

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Characteristic roots for two-lag linear delay differential equations

David M. Bortz^1,

1.
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526

Received: September 30, 2015

Revised: January 31, 2016

Published: September 2016

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Abstract

We consider the class of two-lag linear delay differential equations and develop a series expansion to solve for the roots of the nonlinear characteristic equation. The expansion draws on results from complex analysis, combinatorics, special functions, and classical analysis for differential equations. Supporting numerical results are presented along with application of our method to study the stability of a two-lag model from ecology.

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Mathematics Subject Classification: Primary: 34K99, 65H17; Secondary: 41A58.

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