一类三次捕食者-食饵交错扩散系统解的整体存在性和稳定性(英文)  

Global Existence and Stability of Solutions for a Cubic Predator-Prey System with Cross-Diffusion

作　　者：曹怀火[1] 伏升茂[2] 

机构地区：[1]池州学院数学与计算机科学系,安徽池州247000 [2]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《应用数学》2009年第4期836-842,共7页Mathematica Applicata

基　　金：Supported by the China National Natural Science Foundation (10671158);the NSF of Gansu Province (3ZS061-A25-015);the Scientific Research Fund of Gansu Provincial Education Department (060121);NWNU-KJCXGC-03-18,39 Foundations

摘　　要：首先引进一类三次捕食者-食饵交错扩散系统,该系统是两种群Lotka-Volterra交错扩散系统的推广,现有的已知结果目前很少.本文应用能量估计方法,结合Shauder理论和bootstrap技巧讨论该系统古典整体解的存在唯一性,并在反应函数的系数满足一定条件时,通过构造Lyapunov函数证明系统正平衡点的全局渐近性.This paper firstly proposed a cubic predator-prey cross-diffusion system, which was a generalization of the two-species Lotka-Volterra predator-prey model, as well as very few mathematical results were known for it. Next using energy estimates and the bootstrap arguments, we investigated the global existence of classical solutions for system. Finally, the global asymptotic stability of positive equilibrium point of the system was proved by Lyapunov functions.

关 键 词：三次捕食者-食饵 自扩散 交错扩散 整体存在性 稳定性 

分 类 号：O175.26[理学—数学]