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

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish
Pages (from-to)157-164
Number of pages8
JournalApplied Mathematics and Computation
StatePublished - 1 Jan 2015


  • Global asymptotic stability
  • Linear and nonlinear delay differential equations
  • Mackey-Glass equation of respiratory dynamics

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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