title: Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays.
abstract: In recent years, complex-valued recurrent neural networks have been developed and analysed in-depth in view of that they have good modelling performance for some applications involving complex-valued elements. In implementing continuous-time dynamical systems for simulation or computational purposes, it is quite necessary to utilize a discrete-time model which is an analogue of the continuous-time system. In this paper, we analyse a discrete-time complex-valued recurrent neural network model and obtain the sufficient conditions on its global exponential periodicity and exponential stability. Simulation results of several numerical examples are delineated to illustrate the theoretical results and an application on associative memory is also given.
authors.affiliation: Department of Mathematics, Chongqing Jiaotong University, Chongqing, China. Electronic address: windyvictor@gmail.com.
authors.forename: Jin
authors.initials: J
authors.lastname: Hu
authors.affiliation: Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China. Electronic address: jwang@mae.cuhk.edu.hk.
authors.forename: Jun
authors.initials: J
authors.lastname: Wang
mesh_terms: D016571:Neural Networks, Computer; D010507:Periodicity; D013997:Time Factors
keywords: Complex-valued neural networks; Discrete-time; Exponential periodicity; Exponential stability