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Traveling waves for nonlinear cellular neural networks with distributed delays. (English) Zbl 1228.34122
The authors study traveling waves of a nonlinear cellular neural network model, which is described by a lattice equation with finite or infinite distributed delays. They prove the existence of monostable traveling waves by employing Schauder’s fixed point theorem coupled with the upper and lower solutions method. They also establish the nonexistence of monostable traveling waves and the exponential asymptotic behavior of the obtained monotone wave profiles as the wave coordinate goes to infinity. Their work improves and covers some previous results.

34K31Lattice functional-differential equations
34K10Boundary value problems for functional-differential equations
35C07Traveling wave solutions of PDE
47N20Applications of operator theory to differential and integral equations
92B20General theory of neural networks (mathematical biology)
Full Text: DOI
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