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 Existence and Stability of Antiperiodic Solution for a Class of Generalized Neural Networks with Impulses and Arbitrary Delays on Time Scales | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 132790 19 pages doi 2010 132790 Research Article Existence and Stability of Antiperiodic Solution for a Class of Generalized Neural Networks with Impulses and Arbitrary Delays on Time Scales Yongkun Li Erliang Xu and Tianwei Zhang Department of Mathematics Yunnan University Kunming Yunnan 650091 China Correspondence should be addressed to Tianwei Zhang 1200801347@ Received 14 June 2010 Accepted 16 August 2010 Academic Editor Kok Lay Teo Copyright 2010 Yongkun Li 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. By using coincidence degree theory and Lyapunov functions we study the existence and global exponential stability of antiperiodic solutions for a class of generalized neural networks with impulses and arbitrary delays on time scales. Some completely new sufficient conditions are established. Finally an example is given to illustrate our results. These results are of great significance in designs and applications of globally stable anti-periodic Cohen-Grossberg neural networks with delays and impulses . 1. Introduction In this paper we consider the following generalized neural networks with impulses and arbitrary delays on time scales xA t A t x tỴ B t x tỴ F t xt t 6 T t tk bx tk x t k - x tk Ik x tk t tk k 6 N where T is an o 2-periodic time scale and if t 6 T 0 6 E then t 0 6 T E is a subset of R- -TO 0 A t x t diag a1 t x1 t a2 t x2 t . an t xn t B t x t b1 t X1 f b2 t x2 f . bn t xn t F t xt f1 t xi . fn t xi T fi t xi fi t xu x2t . xnt xit 0 xft 0 t 6 T 0 6 E i 1 2 . n and x tk x t- represent the right and left limits of x tk in the sense of time scales t is a sequence of real numbers such that 0 t1 t2 tn TO as l TO. There exists a positive integer q such that tl q tl w
