Abstract
The dynamics analysis of recurrent neural networks (RNNs) is a first and necessary step for any practical applications of them. In the present paper, the easily verified theorem is found to as certain the asymptotical stability for generic RNN model with projection mapping under the critical condition that a discriminant matrix defined by the networks is semi-positive definite. The results given here not only improve deeply upon the existing relevant critical as well as non-critical dynamics conclusions in literature, but also can be used in the practical application of RNNs directly.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Xu Z B, Qiao H, Peng J, and Zhang B, A comparative study of two modeling approaches in neural networks, Neural Netw., 2004, 17: 73–85.
Qiao H, Peng J, Xu Z B, and Zhang B, A reference model approach to stability analysis of neural networks, IEEE Trans. Syst., Man Cybern., 2003, 33: 925–936.
Peng J, Xu Z B, Qiao H, and Zhang B, A critical analysis on global convergence of Hopfield-type neural networks, IEEE Trans. Circuits Syst., 2005, 52: 804–814.
Qiao C and Xu Z B, Critical dynamics study on recurrent neural networks: Globally exponential stability, {Niteurocomputing}, 2012, 77(1): 205–211.
Yang Y Q and Cao J D, Solving quadratic programming problems by delayed projection neural network, IEEE Trans. Neural Netw., 2006, 17: 1630–1634.
Qiao C and Xu Z B, New critical analysis on global convergence of recurrent neural networks with projection mappings, Lecture Notes in Computer Science, Springer, Berlin, 2007, 131–139.
Qiao C and Xu Z B, A critical global convergence analysis of recurrent neural networks with general projection mappings, {NitNeurocomputing}, 2009, 72: 1878–1886.
Qiao C and Xu z B, On the P-critical dynamics analysis of projection recurrent neural networks, Neurocomputing, 2010, 73: 2783–2788.
Qiao C, Jing W F, and Xu Z B, The UPPAM continuous-time RNN model and its critical dynamics, Neurocomputing, 2013, 106(15): 158–166.
Chua L O and Roska T, Cellular Neural Networks and Visual Computing: Foundations and Applications, Cammridge University Press, U.K., 2002.
Park J, Kim H Y, Park Y, and Lee S W, A synthesis procedure for associative memories based on space-varying cellular neural networks, Neural Netw., 2001, 14: 107–113.
Slavova A, Cellular Neural Networks: Dynamics and Modelling, Kluwer Academic Publishers Pub., 2003.
Hu X L and Wang J, Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems, IEEE Trans. Syst., Man Cybern., 2007, 37: 1414–1421.
Chen T P, Global convergence of delayed dynamical systems, IEEE Trans. Neural Netw., 2001, 12: 1532–1536.
Liu X W and Chen T P, A new result on the global convergence of Hopfield neural networks, IEEE Trans. Circuits Syst., 2002, 49: 1514–1516.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Nature Science Foundation of China under Grant Nos. 11101327, 11471006, and 11171270, the National Basic Research Program of China (973 Program) under Grant No.2013C13329406, the Fundamental Research Funds for the Central Universities under Grant Nos. xjj20100087 and 2011jdhz30.
This paper was recommended for publication by Editor HONG Yiguang.
Rights and permissions
About this article
Cite this article
Qiao, C., Liang, D. & Sun, K. Dynamics analysis for generic projection continuous-time RNNs with bounded matrices. J Syst Sci Complex 28, 799–812 (2015). https://doi.org/10.1007/s11424-015-2053-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-015-2053-4