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

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).