带自扩散和交错扩散的三种群Lotka-Volterra竞争模型解的一致有界性和稳定性  

Uniform Boundedness and Stability of Solutions to the Three-Species Lotka-Volterra Competition Model with Self and Cross-Diffusion

作　　者：伏升茂[1] 高海燕[1] 崔尚斌[2] 

机构地区：[1]西北师范大学数学与信息科学学院,兰州730070 [2]中山大学数学系,广州510275

出　　处：《数学年刊（A辑）》2006年第3期345-356,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10471157);甘肃省自然科学基金(No.ZS031-A25-003-Z)资助的项目

摘　　要：应用能量估计方法和Gagliardo-Nirenberg型不等式,讨论了带自扩散和交错扩散的三种群Lotka-Volterra竞争模型解的一致有界性和整体存在性,并由Lyapunov函数证明了该模型正平衡点的全局渐近稳定性．Using the energy estimates and Cagliardo-Nirenberg inequalities, the uniform boundedness and global existence of solutions to the three-species Lotka-Volterra competition model with self and cross-diffusion are studied. Meanwhile, global asymptotic stability of the positive equilibrium point for the model is proved by Lyapunov function.

关 键 词：自扩散 交错扩散 竞争 一致有界 稳定性 

分 类 号：O175.26[理学—数学]