The aim of this work is to study the existence and stability of traveling wave solutions for discrete-time model of delayed cellular neural networks distributed in the one-dimensional integer lattice 1. Since the dynamics of each given cell depends on its left and right neighboring cells, it is not easy to construct the traveling wave solutions. Using the method of step along with positive characteristic roots of the equations, we successfully prove the existence of traveling wave solutions. Moreover, we show that all the traveling wave solutions are unstable. We also provide some numerical results to support our results, and point out the different structures of traveling wave solutions between the continuous-time and discrete-time models.
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|State||Published - Jun 2013|
- Cellular neural networks
- characteristic root
- method of step