Stability and bifurcation analysis for a single-species discrete model with stage structure

In this paper, a single-species discrete model with stage structure is investigated. By analyzing the corresponding characteristic equations, the local asymptotic stability of non-negative equilibrium points and the existence of flip bifurcation are discussed. Using the center manifold theory, the stability of the non-hyperbolic equilibrium point is obtained. Based on bifurcation theory, we obtain the direction and the stability of a flip bifurcation at the positive equilibrium with the birth rate as the bifurcation parameter. Finally, some numerical simulations, including phase portraits, chaotic bands with period windows, and Lyapunov exponent methods, are performed to validate the theoretical results, which extends the results in previous papers.