Electron. J. Differential Equations, Vol. 2017 (2017), No. 102, pp. 1-13.

Uniqueness of traveling wave solutions for non-monotone cellular neural networks with distributed delays

Hui-Ling Zhou, Zhixian Yu

Abstract:
In this article, we study the uniqueness of traveling wave solutions for non-monotone cellular neural networks with distributed delays. First we establish a priori asymptotic behavior of the traveling wave solutions at infinity. Then, based on Ikehara's theorem, we prove the uniqueness of the solution $\psi(n-ct)$ with $c\leq c_*$, where $c_*<0$ is the critical wave speed.

Submitted March 1, 2017. Published April 11, 2017.
Math Subject Classifications: 35C07, 92D25, 35B35.
Key Words: Cellular neural network; uniqueness; non-monotone; asymptotic behavior; distributed delays.

Show me the PDF file (239 KB), TEX file for this article.

  Hui-Ling Zhou
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: hlzhou@163.com
Zhixian Yu
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: zxyu0902@163.com

Return to the EJDE web page