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Traveling Wave Solutions for Planar Lattice Differential Systems with Applications to Neural Networks

✍ Scribed by Shiwang Ma; Xiaoxin Liao; Jianhong Wu

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
236 KB
Volume
182
Category
Article
ISSN
0022-0396

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✦ Synopsis

We obtain some existence results for traveling wave fronts and slowly oscillatory spatially periodic traveling waves of planar lattice differential systems with delay. Our approach is via Schauder's fixed-point theorem for the existence of traveling wave fronts and via S 1 -degree and equivarant bifurcation theory for the existence of periodic traveling waves. As examples, the obtained abstract results will be applied to a model arising from neural networks and explicit conditions for traveling wave fronts and global continuation of periodic waves will be obtained. # 2002 Elsevier Science (USA)

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