Abstract
Based on considering mature individuals with density dependence, a two-stage structure model of egg-mature individuals with cannibalism is established. The dynamic behavior of the equilibrium of the model is discussed from two aspects: when no cannibalism exists, the global asymptotic stability of the equilibria is proved by the Lyapunov theorem; when cannibalism exists, it makes the model have saddle-node bifurcation by using the center manifold theorem. By constructing Dulac function, there is no limit cycle in the two-dimensional autonomous system, therefore, the global stability of the equilibria is obtained. Finally, the theoretical results are verified by numerical simulation.
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