Wave propagation for a two-component lattice dynamical system arising in strong competition models

作者：Guo Jong Shenq^*; Wu Chang Hong

来源：Journal of Differential Equations, 2011, 250(8): 3504-3533.

DOI：10.1016/j.jde.2010.12.004

• Lattice dynamical system
• Stationary solution
• Propagation failure
• Traveling wave
• Wave speed

We study a Lotka-Volterra type competition system with bistable nonlinearity in which the habitat is divided into discrete niches. We show that there exist non-monotone stationary solutions when the migration coefficients are sufficiently small. Also, we prove that the propagation failure phenomenon occurs. Finally, we focus on the traveling wave with nonzero wave speed. By investigating the asymptotic behavior of tails of wave profiles, we show that nonzero speed wave profiles are monotone. Moreover, the nonzero wave speed is unique in the sense that the wave cannot propagate with two different nonzero wave speeds.

• 出版日期2011-4-15