Copyright © 2009 Jian Jhong Lin and Sui Sun Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Szekeley observed that the dynamic pattern of the locomotion of salamanders can be explained
by periodic vector sequences generated by logical neural networks. Such sequences can
mathematically be described by “doubly periodic traveling waves” and therefore it is of interest
to propose dynamic models that may produce such waves. One such dynamic network model
is built here based on reaction-diffusion principles and a complete discussion is given for the
existence of doubly periodic waves as outputs. Since there are 2 parameters in our model and 4
a priori unknown parameters involved in our search of solutions, our results are nontrivial. The
reaction term in our model is a linear function and hence our results can also be interpreted as
existence criteria for solutions of a nontrivial linear problem depending on 6 parameters.