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

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  • Berezansky, Leonid
  • Braverman, Elena

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.

Suggested Citation

  • Berezansky, Leonid & Braverman, Elena, 2015. "Stability conditions for scalar delay differential equations with a non-delay term," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 157-164.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:157-164
    DOI: 10.1016/j.amc.2014.10.088
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    References listed on IDEAS

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    1. Xia, Yonghui & Wong, Patricia J.Y., 2009. "Global exponential stability of a class of retarded impulsive differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 440-453.
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    Cited by:

    1. Berezansky, Leonid & Domoshnitsky, Alexander & Gitman, Mikhail & Stolbov, Valery, 2015. "Exponential stability of a second order delay differential equation without damping term," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 483-488.

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