Entire solutions with merging fronts to a bistable periodic lattice dynamical system

We are interested in finding entire solutions of a bistable periodic lattice dynamical system. By constructing appropriate super- and subsolutions of the system, we establish two difierent types of merging-front entire solutions. The first type can be characterized by two monostable fronts merging and converging to a single bistable front; while the second type is a solution which behaves as a monostable front merging with a bistable front and one chases another from the same side of x-axis. For this discrete and spatially periodic system, we have to emphasize that there has no symmetry between the increasing and decreasing pulsating traveling fronts, which increases the dificulty of construction of the super- and subsolutions.