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 New Results of a Class of Two-Neuron Networks with Time-Varying Delays | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 648148 14 pages doi 2008 648148 Research Article New Results of a Class of Two-Neuron Networks with Time-Varying Delays Chuangxia Huang 1 Yigang He 2 and Lihong Huang3 1 College of Mathematics and Computers Changsha University of Science and Technology Changsha Hunan 410076 China 2 College of Electrical and Information Engineering Hunan University Changsha Hunan 410082 China 3 College of Mathematics and Econometrics Hunan University Changsha Hunan 410082 China Correspondence should be addressed to Chuangxia Huang cxiahuang@ Received 19 September 2008 Accepted 4 December 2008 Recommended by Marta Garcia-Huidobro With the help of the continuation theorem of the coincidence degree a priori estimates and differential inequalities we make a further investigation of a class of planar systems which is generalization of some existing neural networks under a time-varying environment. Without assuming the smoothness monotonicity and boundedness of the activation functions a set of sufficient conditions is given for checking the existence of periodic solution and global exponential stability for such neural networks. The obtained results extend and improve some earlier publications. Copyright 2008 Chuangxia Huang et al. 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 Neural networks are complex and large-scale nonlinear dynamics while the dynamics of the delayed neural network are even richer and more complicated 1 . To obtain a deep and clear understanding of the dynamics of neural networks one of the usual ways is to investigate the delayed neural network models with two neurons which can be described by differential systems see 2-8 . It is hoped that through discussing the dynamics of .
