Convex dominates concave : An exclusion principle in discrete-time Kolmogorov systems

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Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」We establish an exclusion principle in discrete-time Kolmogorov systems by using average Liapunov functions. The exclusion principle shows that a weakly dominant species with a convex logarithmic growth rate function eliminates species with concave logarithmic growth rate functions. A general result is applied to specific population models. This application gives an improved exclusion principle for the specific population models.