Entire solutions of nonlinear cellular neural networks with distributed time delays

The aim of this work is to study the existence of entire solutions of nonlinear cellular neural networks with distributed time delays (DCNN). The entire solutions are defined in the whole space and for all time $t\in{\mathbb R}$. From Yu et al (2011 J. Diff. Eqns 251 630–50), we know that the DCNN model admits travelling front solutions. Combining the travelling front solutions with different wave speeds and a spatially independent solution of the DCNN model, we establish some new entire solutions to describe the interactions of travelling fronts. Various qualitative features of the entire solutions are also investigated in this work.