This paper investigates a patch structure Nicholson’s blowflies model involving multiple pairs of different time-varying delays. Without assuming the uniform positiveness of the death rate and the boundedness of coefficients, we establish three novel criteria to check the global convergence, generalized exponential convergence and asymptotical stability on the zero equilibrium point of the addressed model, respectively. Our proofs make substantial use of differential inequality techniques and dynamical system approaches, and the obtained results improve and supplement some existing ones. Last but not least, a numerical example with its simulations is given to show the feasibility of the theoretical results.

中文翻译：

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具有多对时变延迟的Nicholson's蝇模型对膜片结构的新稳定性标准

本文研究了涉及多对不同时变延迟的Nicholson's蝇模型的补丁结构。在不假设死亡率均匀一致和系数有界的情况下，我们建立了三个新的标准来分别检验所解决模型的零平衡点的全局收敛性，广义指数收敛性和渐近稳定性。我们的证明充分利用了微分不等式技术和动力学系统方法，所获得的结果改进并补充了一些现有的方法。最后但并非最不重要的是，给出了一个带有其模拟的数值示例，以显示理论结果的可行性。