Paper Info
Title
Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks.
Abstract
The paper considers a general neural network model with impulses at a given sequence of instants, discontinuous neuron activations, delays, and time-varying data and inputs. It is shown that when the neuron interconnections satisfy an M-matrix condition, or a dominance condition, then the state solutions and the output solutions display a common asymptotic behavior as time t--> +infinity. It is also shown, via a new technique based on prolonging the solutions of the delayed neural network to -infinity, that it is possible to select a unique special solution that is globally exponentially stable and can be considered as the unique global attractor for the network. Finally, this paper shows that for almost periodic data and inputs the selected solution is almost periodic; moreover, it is robust with respect to a large class of perturbations of the data. Analogous results also hold for periodic data and inputs. A by-product of the analysis is that a sequence of almost periodic impulses is able to induce in the generic case (nonstationary) almost periodic solutions in an otherwise globally convergent nonimpulsive neural network. To the authors' knowledge the results in this paper are the only available results on global exponential stability of the unique periodic or almost periodic solution for a general neural network model combining three main features, i.e., impulses, discontinuous neuron activations and delays. The results in this paper are compared with several results in the literature dealing with periodicity or almost periodicity of some subclasses of the neural network model here considered and some hints for future work are given.
Year
DOI
Venue
2010
10.1109/TNN.2010.2048759
IEEE Transactions on Neural Networks
Keywords
Field
DocType
matrix algebra,neural nets,M-matrix condition,almost periodicity,common asymptotic behavior,delayed neural networks,discontinuous neural networks,discontinuous neuron activations,dominance condition,globally convergent nonimpulsive neural network,impulsive neural networks,Almost periodic functions,common asymptotic behavior,delays,discontinuous neural networks,global exponential stability,impulses
Attractor,Applied mathematics,Almost periodic function,Computer science,Control theory,Exponential stability,Artificial intelligence,Artificial neural network,Asymptotic analysis,Periodic function,Pattern recognition,Cellular neural network,Periodic graph (geometry)
Journal
Volume
Issue
ISSN
21
7
1941-0093
Citations 
PageRank 
References 
41
1.44
24
Authors
3
Name
Order
Citations
PageRank
Walter Allegretto1657.11
Duccio Papini222610.77
Mauro Forti339836.80