New periodic stability for a class of Nicholson's blowflies models with multiple different delays

Abstract

In this research work, the existence and global exponential stability of the positive periodic solutions of Nicholson’s blowflies equation with multiple different time-varying delays are investigated. Without adopting the restriction assumption on the maximum rate of reproduction function, we establish a criterion to ensure the existence and global exponential stability of the positive periodic solutions for the addressed equation by using differential inequality techniques, the fluctuation lemma and Lyapunov functional method. The obtained result is new, which improves and complements some existing ones. Moreover, the effectiveness of the theoretical finding is illustrated by an example with numerical simulation.