American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 930-939. doi: 10.3934/proc.2005.2005.930

Existence of monotonic traveling waves in modified RTD-based cellular neural networks

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

1. 

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

Received  August 2004 Revised  April 2005 Published  September 2005

We study the existence of monotonic traveling and standing wave solutions of the one-dimensional modified RTD-based cellular neural networks. Employing the techniques of monotone iteration coupled with the concept of upper and lower solutions, we can classify the monotonic traveling and standing waves with various asymptotic boundary conditions. Some numerical examples are also provided.
Keywords: standing waves., traveling waves, lattice differential equations, cellular neural networks, monotone iteration methods.
Mathematics Subject Classification: Primary: 34K10, 34K28; Secondary: 34B1.
Citation: Suh-Yuh Yang, Cheng-Hsiung Hsu. Existence of monotonic traveling waves in modified RTD-based cellular neural networks. Conference Publications, 2005, 2005 (Special) : 930-939. doi: 10.3934/proc.2005.2005.930
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