| 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. |
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