带有比率依赖的Leslie-Gower系统行波解的存在性

发布时间：2018-06-17 13:34

  本文选题：Leslie-Gower系统 + 行波解　； 参考：《东北师范大学》2017年硕士论文

【摘要】：本文研究了带有比率依赖功能反应的扩散Leslie-Gower系统,行波解的存在性.将系统等价变形为R3中的方程组,并给出最小波速c*.当cc*时行波解不存在;当cc*时,用Dunbar所提出的打靶法证明了行波解的存在性.这一方法主要是把Wazewski定理,稳定流形定理及LaS alle不变性原理三者结合起来使用.首先,应用Wazewski定理,构造出一个足够大的Wazewski集,使得解轨线在+∞处满足边界条件,即相空间的解轨线一定位于(u*,v*,0)处的稳定流形上.然后,在(1,0,0)的一个充分小的圆内找到一个Σ集合,并证明存在过Σ的轨线不会离开W中的一个有界区域.利用LaS alle不变性原理证明解轨线趋于正平衡点(u*,v*,0),完成行波解存在性定理的证明.
[Abstract]:In this paper, we study the existence of traveling wave solutions for a diffusive Leslie-Gower system with ratio dependent functional reactions. The system is deformed into the equations in R3, and the minimum wave velocity C ~ (1) is given. The traveling wave solution does not exist at cc* and the existence of traveling wave solution is proved by the shooting method proposed by Dunbar. This method mainly combines Wazewski theorem, stable manifold theorem and LaS alle invariance principle. Firstly, a sufficiently large Wazewski set is constructed by using the Wazewski theorem, so that the solution trajectory satisfies the boundary condition at 鈭，

本文编号：2031235