Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates

The global dynamics of discrete competitive model of Lotka-Volterra type with two species is considered. Earlier works have shown that the unique positive equilibrium is globally attractive under the assumption that the intrinsic growth rates of the two competitive species are less than 1 ln 2, and further the unique positive equilibrium is globally asymptotically stable under the stronger condition that the intrinsic growth rates of the two competitive species are less than or equal to 1. We prove that the system can also be globally asymptotically stable when the intrinsic growth rates of the two competitive species are greater than 1 and globally attractive when the intrinsic growth rates of the two competitive species are greater than 1 ln 2.