Non-autonomous Differential Systems with Delays: A Global Attraction Analysis

Abstract

AbstractIn this paper, we derive criteria of global attractivity of a (possibly constant) positive periodic solution in non-autonomous systems of delay differential equations. Our approach can be viewed as the extension for non-autonomous systems of the folkloric connection between discrete dynamics and scalar delay differential equations. It is worth mentioning that we provide delay-dependent criteria of global attraction that cover the best delay independent conditions. We apply our results to non-autonomous variants of several classical models such that Nicholson’s blowfly equation, Goodwin’s model oscillator, the Mackey–Glass equation and systems with patch structure.