On camel-like traveling wave solutions in cellular neural networks

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• 作者：Hsu ; Cheng-Hsiung ; Yang ; Suh-Yuh
• 关键词：34A12 ; 34B15 ; 34B45 ; 34K10 ; Lattice dynamical systems ; Cellular neural networks ; Camel-like traveling waves ; Oscillating traveling waves
• 刊名：Journal of Differential Equations
• 出版年：2004
• 出版时间：January 20, 2004
• 年：2004
• 卷：196
• 期：2
• 页码：481-514
• 全文大小：686 K

文摘

This paper is concerned with the existence of camel-like traveling wave solutions of cellular neural networks distributed in the one-dimensional integer lattice Z¹. The dynamics of each given cell depends on itself and its nearest m left neighbor cells with instantaneous feedback. The profile equation of the infinite system of ordinary differential equations can be written as a functional differential equation in delayed type. Under appropriate assumptions, we can directly figure out the solution formula with many parameters. When the wave speed is negative and close to zero, we prove the existence of camel-like traveling waves for certain parameters. In addition, we also provide some numerical results for more general output functions and find out oscillating traveling waves numerically.