一类带交错扩散项的捕食-被捕食模型平衡解的存在性和稳定性（英文）  

The Existence and Stability of Steady States for a Prey Predator System

作　　者：徐茜 张莉 Xu Qian;Zhang Li(Department of Basic Courses,Beijing Union University,Beijing 100101,China)

机构地区：[1]北京联合大学基础部,北京100101

出　　处：《南开大学学报（自然科学版）》2018年第5期71-78,共8页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by the National Natural Science Foundation of China(11501031,11471221);Beijing Natural Science Foundation(1152002)

摘　　要：主要研究了一类带交错扩散项的捕食-被捕食模型平衡解的存在性和稳定性.应用全局分岔理论得到正平衡解的存在性.应用谱分析和稳定性理论得到分岔点附近的分岔解的局部稳定性.The existence and stability of steady states for a prey-predator model with cross-diffusion are studied. The existence of the positive steady state solutions is proved by using the global bifurcation theory. The stability of the local bifurcating solution near the bifurcation point is showed by applying the spectral analysis and the principle of exchange of stability.

关 键 词：整体分岔 谱分析 稳定性 

分 类 号：O175.2[理学—数学]