Global exponential periodicity of three-unit neural networks in a ring with time-varying delays

Authors:
Chuangxia Huang;Yigang He;Lihong Huang;Mingyong Lai
Affiliations:
College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, PR China and College of Electrical and Information Engineering, Hunan Universit ...;College of Electrical and Information Engineering, Hunan University, Changsha, Hunan 410082, PR China;College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China;School of Economics and Business, Hunan University, Changsha, Hunan 410082, PR China
Venue:
Neurocomputing
Year:
2008

Citing 9
Cited 1

Original Contribution: Associative memory with nonmonotone dynamics

Neural Networks
Delay induced periodicity in a neural netlet of excitation and inhibition

Physica D
Bifurcations, stability, and monotonicity properties of a delayed neural network model

Physica D
Existence and stability of almost periodic solution for BAM neural networks with delays

Applied Mathematics and Computation
Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays

Neurocomputing
Letters: Stability in static delayed neural networks: A nonlinear measure approach

Neurocomputing
Exponential stability and periodic oscillatory solution in BAM networks with delays

IEEE Transactions on Neural Networks
Time delays and stimulus-dependent pattern formation in periodic environments in isolated neurons

IEEE Transactions on Neural Networks
How delays affect neural dynamics and learning

IEEE Transactions on Neural Networks

Properties of variations in the periods of ring neural oscillators with noise

Neurocomputing

Quantified Score

Hi-index	0.01

Visualization

Abstract

This paper formulates and studies a model of three-unit neural networks in a ring. The model can well describe many practical architectures of delayed neural networks, which is generalization of some existing neural networks under a time-varying environment. Without assuming the boundedness, monotonicity, and differentiability of activation functions and any symmetry of interconnections, we establish some sufficient conditions for checking the existence of periodic solution and global exponential stability for the neural networks. A continuation theorem of the coincidence degree and inequality analysis are employed. Our results are all independent of the delays and maybe more convenient to design a circuit network.