具有阶段结构的Lotka-Volterra合作系统的稳定性和行波解  

Stability and Traveling Fronts in Lotka-Volterra Cooperation Model with Stage Structure

作　　者：吴事良[1] 李万同[2] 

机构地区：[1]西安电子科技大学应用数学系,西安710071 [2]兰州大学数学与统计学院,兰州730000

出　　处：《数学物理学报（A辑）》2008年第3期454-464,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10571078);教育部教学科研奖励计划项目资助

摘　　要：该文建立并研究了一个两物种成年个体相互合作的时滞反应扩散模型.利用线性化稳定性方法和Redlinger上、下解方法证明了该模型具有简单的动力学行为,即零平衡点和边界平衡点是不稳定的,而唯一的正平衡点是全局渐近稳定的.同时,利用Wang,Li和Ruan建立的具有非局部时滞的反应扩散系统的波前解的存在性,证明了该模型连接零平衡点与唯一正平衡点的波前解的存在性.In this paper, the authors derive and study a delayed diffusion system, which models the interaction between the two species, the adult members of which are in cooperation. By using the method of sub- and super-solutions due to Redlinger, we show that the diffusive delay model generates simple global dynamics, i.e., the zero steady state and the boundary equilibria are linear unstable and the unique positive steady state is globally asymptotically stable. We also establish the existence of traveling wave fronts connecting the zero solution of this equation with the unique positive steady state. The approach used in this paper is the upper-lower solutions technique and the monotone iteration recently developed by Wang, Li and Ruan for reaction-diffusion systems with spatio-temporal delays.

关 键 词：合作 时滞 波前解 全局稳定性 阶段结构 反应扩散方程 

分 类 号：O175.14[理学—数学]