离散型三维竞争系统正平衡点的渐近稳定性  

Asymptotic stability of positive equilibrium point in discrete three-dimensional competitive system

作　　者：杨鑫逾 杨逢建 YANG Xinyu;YANG Fengjian(School of Mathematics and Computational Science,Hunan University of Science and Technology,Xiangtan 411021,China;Retirement Department,Zhongkai University of Agriculture and Engineering,Guangzhou 510225,China)

机构地区：[1]湖南科技大学数学与计算科学学院,湖南湘潭411021 [2]仲恺农业工程学院离退休干部工作处,广东广州510225

出　　处：《仲恺农业工程学院学报》2023年第2期39-43,共5页Journal of Zhongkai University of Agriculture and Engineering

摘　　要：研究了离散型三维竞争系统中正平衡点的存在条件和渐近稳定性,得到了这类竞争系统中正平衡点存在的充分必要条件,获得了正平衡点渐近稳定的几个充分条件,得到了正平衡点不渐近稳定的几个区域,由此得到了参与竞争的各群体和谐共生的条件和永不和谐的条件.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.

关 键 词：竞争系统 正平衡点 渐近稳定性 

分 类 号：O175.13[理学—数学]