Periodicity and exponential stability of discrete-time neural networks with variable coefficients and delays

Advances in Difference Equations

Ranchao Wu¹  Hui Xu² 

[1] Department of Public Teaching, Anhui Business Vocational College, Hefei, China;School of Mathematics, Anhui University, Hefei, China

关键词: coincidence degree;    discrete neural networks;    variable coefficient;    exponential stability;    periodic solution;    M-matrix;   

DOI  :  10.1186/1687-1847-2013-226

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Discrete analogues of continuous-time neural models are of great importance in numerical simulations and practical implementations. In the current paper, a discrete model of continuous-time neural networks with variable coefficients and multiple delays is investigated. By Lyapunov functional, continuation theorem of topological degree, inequality technique and matrix analysis, sufficient conditions guaranteeing the existence and globally exponential convergence of periodic solutions are obtained, without assuming the boundedness and differentiability of activation functions. To show the effectiveness of our method, an illustrative example is presented along with numerical simulations. MSC:34D23, 34K20, 39A12, 92B20.

【 授权许可】

CC BY