Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Doubly Periodic Traveling Waves in a Cellular Neural Network with Linear Reaction | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 243245 29 pages doi 2009 243245 Research Article Doubly Periodic Traveling Waves in a Cellular Neural Network with Linear Reaction Jian Jhong Lin and Sui Sun Cheng Department of Mathematics Tsing Hua University Hsinchu 30043 Taiwan Correspondence should be addressed to Sui Sun Cheng sscheng@ Received 4 June 2009 Accepted 13 October 2009 Recommended by Roderick Melnik 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. Copyright 2009 J. J. Lin and S. S. 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. 1. Introduction Szekely in 1 studied the locomotion of salamanders and showed that a bipolar neural network may generate dynamic rhythms that mimic the sequential contraction and relaxation of four muscle pools that govern the movements of these animals. What is interesting is that we may explain the correct sequential rhythm by means of the transition of state values of four different artificial neurons and the sequential .
