Traveling wave solutions in cellular neural networks with multiple time delays

Cheng-Hsiung Hsu; Suh-Yuh Yang

doi:10.3934/proc.2005.2005.410

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2005, Volume 2005: 410-419. Doi: 10.3934/proc.2005.2005.410 open access

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Traveling wave solutions in cellular neural networks with multiple time delays

Cheng-Hsiung Hsu^1, and
Suh-Yuh Yang^1,

1.
Department of Mathematics, National Central University, Chung-Li 32054

Received: July 31, 2004

Revised: February 28, 2005

Published: August 2005

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Abstract

This work investigates the existence of traveling wave solutions of the cellular neural network distributed in $\mathbb{Z}^1$ with multiple time delays. Applying the method of step with the help of the characteristic function, we can figure out an analytic solution in an explicit form with many parameters. We then focus on the mechanism for producing the so-called camel-like traveling wave solutions and study the effect of delays on the shape of solutions. Some numerical results are also provided to demonstrate the theoretical analysis.

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Mathematics Subject Classification: Primary: 34K10, 34K28; Secondary: 34B15.

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