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Saddle-point Behavior of A Gilpin-Ayala Two-Species Competition Model with Stage Structure
XIZHUANG XIE
Keywords:Gilpin-Ayala, Saddle-point behavior, Competition, Stage structure, Monotone semiflow;
Abstract:
      The saddle-point behavior is considered for a Gilpin-Ayala two- species competition model with stage structure. By the theory of generalized saddle-point behavior proposed by Jiang et al. [6], it is shown that there ad- mits an invariant and one-codimensional C1-separatrix $\Gamma$, which separates the basins of attraction of the two locally stable equilibria such that Species 1 wins the competition whenever the initial data is below $\Gamma$, while Species 2 wins whenever the initial data is above $\Gamma$. Finally, we conclude the paper with some numerical simulations to illustrate the main theoretical results.