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Abstract
This work investigates the structure of a class of traveling wave
solutions of delayed cellular neural networks distributed in the
one-dimensional integer lattice $\mathbb Z^1$.
The dynamics of a given cell is characterized by instantaneous
self-feedback and neighborhood interaction with its two left
neighbors in which one is instantaneous and the other is
distributively delayed due to, for example, finite switching
speed and finite velocity of signal transmission.
Applying the method of step with the aid of positive roots of the
corresponding characteristic function of the profile equation,
we can directly figure out the solution in explicit form.
We then partition the parameter space $(\alpha, \beta)$-plane
into four regions such that the qualitative properties of
traveling waves can be completely determined for each region.
In addition to the existence of monotonic traveling wave
solutions, we also find that, for certain parameters,
there exist non-monotonic traveling wave solutions
such as camel-like waves with many critical points.
Mathematics Subject Classification: 34B15, 34B45, 34K10, 34K28.
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