This paper is intended to investigate a class of Nicholson’s blowflies system with patch structure and multiple pairs of distinct time-varying delays, we are interested in finding the influence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior. By using the theory of functional differential equations, the fluctuation lemma, and the technique of differential inequalities, some new delay-dependent criteria on the global attractivity of the positive equilibrium point are established. In addition, the effectiveness and feasibility of the theoretical achievements are illustrated by some numerical simulations.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.