| 一类具有种内竞争率的竞争扩散模型稳态解的存在性和稳定性 |
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| 引用本文： | 魏美华,常金勇,张巧卫.一类具有种内竞争率的竞争扩散模型稳态解的存在性和稳定性[J].数学的实践与认识,2014(15). |
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| 作者姓名： | 魏美华 常金勇 张巧卫 |
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| 作者单位： | 榆林学院数学与统计学院;中国科学院信息工程研究所; |
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| 基金项目： | 国家自然科学基金(11271236);陕西省教育厅科研计划资助项目(12JK0886);榆林学院博士科研启动基金项目(13GK04);榆林市产学研合作项目(2012cxy3-30) |
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| 摘 要： | 利用Lyapunov-Schmidt约化方法和扰动理论,研究了一类带有不同种内竞争率的两物种竞争扩散模型.首先给出了半平凡稳态解的存在性和稳定性的充分条件,表明在一定条件下新物种可以入侵.在此基础上进一步证实了共存态的存在性和稳定性,研究表明在适当条件下相互竞争的两物种能够共存.所得结果改进和完善了已有的工作.
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| 关 键 词： | 竞争扩散模型 Lyapunov-Schmidt约化方法 存在性 稳定性 |
Existence and Stability of Steady States for a Competition-Diffusion Model with Intraspecific Competition Rates |
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| Abstract: | A competition-diffusion model of two species with different intraspecific competition rates is studied by Lyapunov-Schmidt reduction technique and perturbation theory.The sufficient conditions of existence and stability of semi-trivial steady states are given,which show the invasion of new species.On this basis,the coexistence states and their stability are further investigated,which give appropriate conditions to ensure the coexistence of two competing species.In addition,some known results are improved and perfected by the theoretical analysis. |
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| Keywords: | competition-diffusion model Lyapunov-Schmidt reduction technique existence stability |
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