Stability conditions for scalar delay differential equations with a nondelay term

TL;DR

This paper investigates the stability of scalar delay differential equations with non-delay terms, establishing conditions under which stability is preserved or lost, and applies these results to a respiratory dynamics model.

Contribution

It provides new stability criteria for equations with both delay and non-delay terms, highlighting how non-delay terms can affect stability.

Findings

Non-delay terms with non-negative coefficients can destabilize delay equations.

Sufficient conditions for exponential stability of linear delay equations are derived.

Global attractivity conditions are established for nonlinear delay equations.

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 tothe Mackey-Glass model of respiratory dynamics.