title: Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays.
abstract: In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen-Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results.
authors.affiliation: College of Mathematics and Econometrics, Hunan University, 410082, Changsha, Hunan, PR China; School of Mathematical Sciences, Huaqiao University, 362021, Quanzhou, Fujian, PR China. Electronic address: wds-03@163.com.
authors.forename: Dongshu
authors.initials: D
authors.lastname: Wang
authors.affiliation: College of Mathematics and Econometrics, Hunan University, 410082, Changsha, Hunan, PR China; Hunan Women's University, 410004, Changsha, Hunan, PR China. Electronic address: lhhuang@hnu.edu.cn.
authors.forename: Lihong
authors.initials: L
authors.lastname: Huang
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D010507:Periodicity; D013997:Time Factors
keywords: Cohen–Grossberg neural networks; Differential inclusion; Discontinuous neuron activation; Global exponential stability; Periodicity