Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions

IEEE Transactions on Neural Networks
Zhang Yi, Kok Kiong Tan

Abstract

This paper studies the multistability of a class of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions. It addresses the nondivergence, global attractivity, and complete stability of the networks. Using the local inhibition, conditions for nondivergence are derived, which not only guarantee nondivergence, but also allow for the existence of multiequilibrium points. Under these nondivergence conditions, global attractive compact sets are obtained. Complete stability is studied via constructing novel energy functions and using the well-known Cauchy Convergence Principle. Examples and simulation results are used to illustrate the theory.

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Citations

May 5, 2010·Neural Computation·Wei Zhou, Jacek M Zurada
Oct 6, 2012·Neural Networks : the Official Journal of the International Neural Network Society·Lili Wang, Tianping Chen
Jun 22, 2012·Neural Networks : the Official Journal of the International Neural Network Society·Wei Zhou, Jacek M Zurada
Feb 1, 2011·Neural Networks : the Official Journal of the International Neural Network Society·Eva Kaslik, Seenith Sivasundaram
Dec 5, 2009·Neural Networks : the Official Journal of the International Neural Network Society·Lili WangTianping Chen
Jun 13, 2013·IEEE Transactions on Cybernetics·Zhenkun HuangChang-Yuan Cheng
May 9, 2014·IEEE Transactions on Neural Networks and Learning Systems· Bo Zhou, Qiankun Song
May 9, 2014·IEEE Transactions on Neural Networks and Learning Systems·Zhenyuan GuoZheng Yan
May 9, 2014·IEEE Transactions on Neural Networks and Learning Systems·Mohamad MostafaJürgen Lindner
Jul 22, 2006·IEEE Transactions on Neural Networks·Sebastian WengHelge Ritter
Jan 20, 2009·IEEE Transactions on Neural Networks·Jiali YuLei Zhang
May 9, 2009·IEEE Transactions on Neural Networks·Zhang YiKok Kiong Tan
Dec 14, 2005·IEEE Transactions on Neural Networks·Zhang YiKok Kiong Tan
Sep 28, 2006·IEEE Transactions on Neural Networks·Zhigang Zeng, Jun Wang
Aug 28, 2009·IEEE Transactions on Neural Networks·Lili WangTianping Chen
Feb 1, 2012·IEEE Transactions on Neural Networks and Learning Systems·Zhigang Zeng, Wei Xing Zheng
Aug 17, 2010·IEEE Transactions on Neural Networks·Sung Hwan WonCheol Hoon Park
Sep 9, 2011·IEEE Transactions on Neural Networks·Xiaobing Nie, Jinde Cao
Aug 16, 2015·IEEE Transactions on Neural Networks and Learning Systems·Xiaobing Nie, Wei Xing Zheng
Jul 1, 2015·IEEE Transactions on Neural Networks and Learning Systems·Chih-Lyang Hwang, Chau Jan
Mar 24, 2017·IEEE Transactions on Neural Networks and Learning Systems·Jianyong WangZhang Yi
Jun 11, 2017·IEEE Transactions on Neural Networks and Learning Systems·Xiaofeng ChenYurong Liu
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Matthew S CaudillRalf Wessel
Nov 8, 2019·Neural Networks : the Official Journal of the International Neural Network Society·Peng WanShuang Jin
Feb 1, 2020·Neural Networks : the Official Journal of the International Neural Network Society·Hao ZhangZhigang Zeng
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F R Ruiz-Oliveras, A N Pisarchik

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