Lin Guo, Li Wan-Tong, Ruan Shigui
School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People's Republic of China.
J Math Biol. 2011 Feb;62(2):165-201. doi: 10.1007/s00285-010-0334-z. Epub 2010 Feb 26.
This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species while the spreading speed of the other species is distinctly slower compared to the case when the interspecific competition disappears. Our results also show that the interspecific competition does affect the spread of both species so that the eventual population densities at the coexistence domain are lower than the case when the competition vanishes.
本文关注离散时间递归系统的传播速度和行波解，该系统描述了两种竞争入侵物种的空间传播模式。我们首先建立了波速大于给定阈值时行波解的存在性。此外，我们证明该阈值是一个物种的传播速度，而另一个物种的传播速度与种间竞争消失时的情况相比明显较慢。我们的结果还表明，种间竞争确实会影响两个物种的扩散，使得共存区域最终的种群密度低于竞争消失时的情况。
