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Existence and multiplicity of traveling waves in a lattice dynamical system. (English) Zbl 0954.34029
Summary: The authors prove existence and multiplicity results of monotone traveling wave solutions to some lattice differential equations by using the monotone iteration method. The results include the model of cellular neural networks (CNN). In addition to the monotone traveling wave solutions, nonmonotone and oscillating traveling wave solutions in the delay type of CNN are obtained.

MSC:
34C15Nonlinear oscillations, coupled oscillators (ODE)
92B20General theory of neural networks (mathematical biology)
34C12Monotone systems
34K11Oscillation theory of functional-differential equations
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