Global asymptotic stability for a nonlinear density-dependent mortality Nicholson’s blowflies system involving multiple pairs of time-varying delays

Abstract

In our article, a nonlinear density-dependent mortality Nicholson's blowflies system with patch structure has been investigated, in which the delays are time-varying and multiple pairs. Based upon the fluctuation lemma and differential inequality techniques, some sufficient conditions are found to ensure the global asymptotic stability of the addressed model. Moreover, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained findings, and our consequences are new even when the considered model degenerates to the scalar Nicholson's blowflies equation.

Dynamics in a Nonautonomous Nicholson-Type Delay System

“…It is well known that system (1) not only has profound practical significance but also will enrich and perfect the models on the Nicholson blowflies to some extent. From the published papers [4][5][6][7][8][9][10][11][12][13][14][15][16], we can also find several other similar interesting models on the Nicholson blowflies. For example, Saker and Agarwal [4] studied the periodic solution of the following nonautonomous periodic Nicholson's blowfly system:…”