Wave propagation for a reaction–diffusion model with a quiescent stage on a 2D spatial lattice

Traveling wave solutions in a class of higher dimensional lattice differential systems with delays and applications

“…Now we recall some conclusions about the traveling waves of different dimensional lattice equations with or without delays. In past few years, great progress has been made in the traveling wave solutions for a single equation, see [1], [2], [3], [4], [5], [6], [8], [10], [11], [16], [17], [18], [25], [20], [21], [22], [24], [26], [27], [29] for 1 or 2 dimensional lattices and [19], [23], [28] for higher dimensional lattices. Recently, many authors also paid their attention to the traveling waves for systems with two equations.…”

Traveling wave solutions in a higher dimensional lattice competition-cooperation system with stage structure

“…Lattice differential equations are the discrete versions of reaction-diffusion equations. In past few years, many authors have paid their attention on the existence of traveling wave solutions for lattice differential equations, see [3,4,7,8,13,16,17,21] for one or two dimensional lattices and [15,20,22] for higher dimensional lattices, and also see the results for reaction-diffusion equations with or without stage structure [1,2,5,6,9,10,14,18,19].…”

Traveling wave solutions in delayed higher dimensional lattice differential systems with partial monotonicity

“…Lattice differential equations are discrete versions of reaction-diffusion equations. In recent years, there have been many important results about the existence of traveling wave solutions in lattice differential equations, including delayed or nodelayed equations, see [1][2][3][4][5][6]8,9,13,[17][18][19]21,23,24,26,[28][29][30]32] for a single equation on 1D or 2D lattices, see also [22,25] for cellular neural networks. The authors [20,27,31] considered the existence, uniqueness, stability of equations on higher dimensional lattices.…”