Global exponential stability of a generalized non-autonomous Nicholson’s blowflies model with three time-varying delays

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Abstract

This paper investigated the asymptotic behavior of a generalized Nicholson’s blowflies model characterized by nonautonomous coefficients and three distinct time-varying delays. The dynamics of the population were governed by the following delay differential equation:

$x^{\prime}(t)=-p_{1}(t) x\left(t-h_{1}(t)\right)+p_{2}(t) x\left(t-h_{2}(t)\right) e^{-p_{3}(t) x\left(t-h_{3}(t)\right)} .$

Using a rigorous analytical approach, we established new sufficient conditions that guaranteed the global exponential stability of the zero equilibrium. These conditions provided valuable insights into scenarios of population extinction or suppression under fluctuating environmental influences. Our results extended and improved upon existing literature by incorporating three independent delays h₁(t), h₂(t), and h₃(t), offering a more comprehensive framework for understanding the complex feedback mechanisms in biological systems. To illustrate the practical applicability of our theoretical findings, a numerical example demonstrated the convergence of solutions toward the equilibrium, confirming the robustness of the stability criteria under various conditions.

Keywords

Nicholson’s blowflies model / time-varying delays / non-autonomous coefficients / global exponential stability / asymptotic behavior / delay differential equations

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