三物种竞争-扩散系统双稳行波解的波速符号

在双稳竞争-扩散模型中,由于行波解的波速符号可以预测哪些物种更具有优势并最终占据整个栖息地,因此研究行波解的波速符号具有重要的生物学意义.首先将三物种种群Lotka-Volterra竞争-扩散系统转化为合作系统.然后运用比较原理得到双稳波速与波廓方程特定上下解波速的比较原理.最后根据比较原理以及构造合适的上下解，得到一些判断双稳行波解波速符号的充分条件.这些结果能够更好地预测和控制生物种群的竞争结果.

The Wave Speed Signs for Bistable Traveling Wave Solutions in 3-Species Competition-Diffusion Systems

In the bistable competition-diffusion model, the wave speed signs for the traveling waves can predict which species are more dominant and will eventually occupy the whole habitat. Therefore, it is of great biological significance to study the speed signs for the traveling waves. Firstly, the Lotka-Volterra competition-diffusion system was transformed into a cooperative system. Under the comparison principle, the comparison theorem for the bistable wave speed and the specific upper-lower solution wave speeds of wave profile equations was obtained. Then, according to the comparison theorem and through construction of suitable upper-lower solutions, some sufficient conditions for determining the bistable traveling wave speed signs were obtained. The results help predict and control the competition results of biological populations.