# American Institute of Mathematical Sciences

October  2016, 21(8): 2409-2422. doi: 10.3934/dcdsb.2016053

## Characteristic roots for two-lag linear delay differential equations

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

Received  October 2015 Revised  February 2016 Published  September 2016

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.
Citation: David M. Bortz. Characteristic roots for two-lag linear delay differential equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2409-2422. doi: 10.3934/dcdsb.2016053
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##### References:
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