In this paper, we revisit a Nicholson's blowflies model with proportional delay, the stability and bifurcation of whose discrete version have not been studied. By using the method of semidiscretization, we dig deeply out the stability and Neimark–Sacker bifurcation of its discrete model. Especially, some results for the existence and stability of Neimark–Sacker bifurcation are derived by using the centre manifold theorem and bifurcation theory. Numerical simulations are also formulated to verify the existence of Neimark–Sacker bifurcation derived.

中文翻译：

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具有比例延迟的离散Nicholson's蝇蝇模型的稳定性和Neimark-Sacker分叉

在本文中，我们将重新考虑具有比例延迟的Nicholson的blow蝇模型，尚未研究其离散版本的稳定性和分叉。通过使用半离散化方法，我们深入研究了离散模型的稳定性和Neimark-Sacker分叉。尤其是，利用中心流形定理和分岔理论，得出了有关Neimark-Sacker分岔的存在和稳定性的一些结果。还建立了数值模拟，以验证所产生的Neimark-Sacker分叉的存在。