Traveling Wave Solutions in a One-Dimension Theta-Neuron Model

Authors:
Guoguang Wen;Yongguang Yu;Zhaoxia Peng;Wei Hu
Affiliations:
Department of Mathematics, Beijing Jiaotong University, Beijing, P.R. China 100044;Department of Mathematics, Beijing Jiaotong University, Beijing, P.R. China 100044;Department of Mathematics, Beijing University of Technology, Beijing, P.R. China 100124;Department of Mathematics, Beijing Jiaotong University, Beijing, P.R. China 100044
Venue:
ISNN '09 Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks
Year:
2009

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Abstract

This paper mainly investigates traveling wave solutions in a one dimension theta-neuron model. We derive an analytical lower bound of synaptic coupling strength for traveling waves to exist. Using the numerical simulation methods, we verify some related results on the existence of traveling waves and its dependence on parameters, and give the solutions of traveling waves numerically. Furthermore, the change of the solutions curve of traveling wave is investigated corresponding to the variance of each parameter. Finally, there is an interesting phenomenon that the curve of the solution jumps with the increase of each parameter.