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Traveling Wave Solutions for Planar Lattice Differential Systems with Applications to Neural Networks |
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| Authors: | Shiwang MaXiaoxin Liao Jianhong Wu |
| Institution: | Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai, 200030, People's Republic of Chinaf1shiwangm@163.netf1 Department of Automatic Control, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China Department of Mathematics and Statistics, York University, North York, Ontario, Canada, M3J 1P3 |
| Abstract: | 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 S1-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. |
| Keywords: | planar lattice differential system traveling wave front periodic traveling wave fixed-point theorem S1-degree equivariant bifurcation theory neural network |
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