We study the minimal speed for a two species competition system with monostable nonlinearity. We are interested in the linear determinacy for the minimal speed in the sense defined by (Lewis et al. J Math Biol 45:219–233, 2002). We provide more general cases for the linear determinacy than that of (Lewis et al. J Math Biol 45:219–233, 2002). For this, we study the minimal speed for the corresponding lattice dynamical system. Our approach gives one new way to study the traveling waves of the parabolic equations through its discretization which can be applied to other similar problems.
Journal of Dynamics and Differential Equations 23(2), pp.353-363