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Existence of traveling wave solutions in nonlinear delayed cellular neural networks. (English) Zbl 1154.34364
Summary: This paper is concerned with the existence of traveling wave solutions of cellular neural network systems distributed in the one-dimensional lattice $\Bbb Z$. The dynamics of each given cell depends on itself and its nearest right neighbor cell where delays exist in self-feedback and neighborhood interaction. Under appropriate assumptions, we can prove the existence of traveling wave solutions whose output function is not piecewise linear.

MSC:
34K05General theory of functional-differential equations
34B45Boundary value problems for ODE on graphs and networks
92B20General theory of neural networks (mathematical biology)
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References:
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