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Traveling wave solutions in cellular neural networks with multiple time delays

Pages: 410 - 419, Issue Special, August 2005

 Abstract        Full Text (178.9K)              

Cheng-Hsiung Hsu - Department of Mathematics, National Central University, Chung-Li 32054, Taiwan (email)
Suh-Yuh Yang - Department of Mathematics, National Central University, Chung-Li 32054, Taiwan (email)

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.

Keywords:  lattice differential equations, cellular neural networks, time delays, method of step, camel-like traveling waves.
Mathematics Subject Classification:  Primary: 34K10, 34K28; Secondary: 34B15.

Received: August 2004;      Revised: March 2005;      Published: September 2005.