Stability conditions for scalar delay differential equations with a non-delay term

Leonid Berezansky and Elena Braverman

Applied Mathematics and Computation, 2015, vol. 250, issue C, 157-164

Abstract: The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that introducing a non-delay term with a non-negative coefficient can destroy stability of the delay equation. Next, sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained. The nonlinear results are applied to the Mackey–Glass model of respiratory dynamics.

Keywords: Linear and nonlinear delay differential equations; Global asymptotic stability; Mackey–Glass equation of respiratory dynamics (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:250:y:2015:i:c:p:157-164

DOI: 10.1016/j.amc.2014.10.088

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