一类格竞争系统的双稳周期行波解

Bistable Periodic Traveling Wave Solutions to Lattice Competitive Systems

该文研究了一类格竞争系统的双稳周期行波解的存在性.首先,将两种群竞争系统转化为合作系统;其次,构造合作系统的上下解,并建立比较原理,得到当初始函数满足一定条件时,解在无穷远处是收敛的;最后,利用黏性消去法证明系统连接两个稳定周期平衡点的行波解的存在性.

The existence of bistable periodic traveling wave solutions to lattice competitive systems was studied.Firstly,the lattice competitive system of 2 species was transformed into a cooperative system.Then,the principle of comparison was established and a pair of upper and lower solutions were given to obtain the convergence of the solution at infinity,with the initial function satisfying certain conditions.By means of the vanishing viscosity method and the principle of comparison,the existence of the traveling wave solution connecting 2 stable periodic equilibrium points of the system,was proved.