Existence of traveling wavefront for discrete bistable competition model (Q717943)

The following two-component lattice dynamical system \[ \begin{cases} \frac{du_j}{dt} = (u_{j+1}+u_{j-1}-2u_j) + a u_j(1-u_j-kv_j), \\ \frac{dv_j}{dt} = d(v_{j+1}+v_{j-1}-2v_j) + b v_j(1-v_j-hu_j) \end{cases} \] is studied, where \(u_j=u_j(t)\), \(v_j=v_j(t)\), \(t \in {\mathbb R}\), \(j \in {\mathbb Z}\), \(d>0\), \(h>1\), \(k>1\), \(a>0\) and \(b>0\). The existence of a traveling wavefront solution is established.