Global asymptotic stability of a scalar delay Nicholson's blowflies equation in periodic environment

Abstract

This paper is considered with a scalar delay Nicholson's blowflies equation in periodic environments. By taking advantage of some novel differential inequality techniques and the fluctuation lemma, we set up the sharp condition to characterize the global asymptotic stability of positive periodic solutions on the addressed equation. The obtained results improve and supplement some existing ones in recent literature, and then give a more perfect answer to an open problem proposed by Berezansky et al. in [Appl. Math. Model. 34(2010) 1405–1417]. In particular, two numerical examples are provided to verify the reliability and feasibility of the theoretical findings.