Existence and stability of traveling wave solutions for multilayer cellular neural networks

Stability analysis of traveling wave solutions for lattice reaction-diffusion equations

“…In the past years, there are many literature devoted to the study of existence and stability problems for traveling wave solutions of various continuous reaction-diffusion systems, see e.g., [3,6,19,21,22] and references cited therein. As for lattice differential systems, most literature concentrate on the existence problem of traveling wave solutions, see [4,8,9,11,15,24,26,29]. To the best of our knowledge, there only have limited papers considering the stability problems of traveling wave solutions for lattice differential systems, cf.…”

“…To the best of our knowledge, there only have limited papers considering the stability problems of traveling wave solutions for lattice differential systems, cf. [11,13,25]. Hence, this gives us the main motivation to consider the stability problem for the general system (1).…”