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Abstract The existence conditions and stability of positive equilibrium point in discrete three-dimensional competitive system is discussed. The necessary and sufficient condition of existence for the positive equilibrium point in such competition system is obtained. Some sufficient conditions of asymptotic stability for the positive equilibrium point are established. Some areas are obtained such that the positive equilibrium point is no asymptotic stable in it. At the same time,conditions of never harmony of the groups and harmony symbios of the groups in this competitive system are established.
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2023, Vol. 36 
