On Bifurcation of a Single‐Species Model With Stage Structure and Harvest

ABSTRACT In this paper, the Nicholson's blowflies equation with stage structure and harvest is investigated. By employing the property of Lambert 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 single‐species model are obtained. Furthermore, it is found that when the harvest rate is sufficiently small, the directions of the Hopf bifurcations at the first and last bifurcation values are forward and backward, respectively, and the bifurcating periodic solutions are all asymptotically stable. Numerical simulations are carried out to illustrate the theoretical analysis.