标题： 关于具有收获的阶段结构单一物种模型的分歧 显示英文标题

标题： On bifurcation of a stage-structured single-species model with harvest

摘要： 本文研究了具有阶段结构和收获的 Nicholson 蝇方程的动力学。 通过利用Lambert W函数的性质，得到了正平衡点的存在性。 借助特征方程的特征值分布，得到了单种群模型平衡点的局部稳定性和Hopf分岔的存在性。 此外，根据Balazs I. 和 Rost G.（International Journal of Bifurcation and Chaos 31(2021):2150071）的结果，在收获率足够小时，第一个和最后一个分岔值处的Hopf分岔方向分别为前向和后向，且分岔出的周期解均为渐近稳定的。 最后，进行了数值模拟以验证理论结论。 这些结果可以看作是Shu等人（Journal of Differential Equations 255 (2013) 2565）工作的补充。 显示英文摘要

摘要： This paper investigates the dynamics of the Nicholson's blowffies equation with stage structure and harvest. By employing the property of Lambert W function, the existence of positive equilibria is obtained. With aid of the distribution of the eigenvalues in the characteristic equation, the local stability of the equilibria and the existence of Hopf bifurcation of the singlespecies model are obtained. Furthermore, by applying the results due to Balazs I., Rost G. (Internat. J. Bifur. Chaos 31(2021):2150071), when the harvest rate is sufffciently small, the direction of the Hopf bifurcations at the ffrst and last bifurcation values are forward and backward, respectively, and the bifurcating periodic solutions are all asymptotically stable. Finally, Numerical simulations are conducted to validate the theoretical conclusions. These results can be seen as the complement of the works of Shu et al. (J. Differential Equations 255 (2013) 2565).