[1]陈晓丰,谭远顺,况 杨.具有不连续激励函数的神经网络的多稳定性[J].南京师大学报(自然科学版),2013,36(03):16-20.
 Chen Xiaofeng,Tan Yuanshun,Kuang Yang.Multistability of Neural Networks With Discontinuous Activation Functions[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(03):16-20.
点击复制

具有不连续激励函数的神经网络的多稳定性()
分享到:

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年03期
页码:
16-20
栏目:
数学
出版日期:
2013-09-30

文章信息/Info

Title:
Multistability of Neural Networks With Discontinuous Activation Functions
作者:
陈晓丰1谭远顺1况 杨2
(1.重庆交通大学理学院,重庆 400074) (2.重庆交通大学土木建筑学院,重庆 400074)
Author(s):
Chen Xiaofeng1Tan Yuanshun1Kuang Yang2
(1.School of Science,Chongqing Jiaotong University,Chongqing 400074,China) (2.School of Civil Engineering and Architecture,Chongqing Jiaotong University,Chongqing 400074,China)
关键词:
神经网络多稳定性指数稳定不连续激励函数
Keywords:
neural networksmultistabilityexponential stabilitydiscontinuous activation functions
分类号:
O175.13
摘要:
讨论了一类具有不连续激励函数的神经网络多个平衡点的共存性和稳定性,利用Brouwer不动点原理,给出了多个平衡点同时存在的充分条件,利用构造Lyapunov函数和矩阵不等式技巧,给出了系统平衡点局部指数稳定的判别准则,并对获得的结果进行数值仿真实验,验证其有效性.
Abstract:
The problem on multistability of equilibria is investigated for a class of neural networks with discontinuous activation functions.By using Brouwer’s fixed-point theorem and constructing an appropriate Lyapunov-Krasovskii functional and the matrix inequality techniques,some new criterions for checking the existence,and local exponential stability of equilibria are derived.One simulation example is given to show the effectiveness of the proposed result.

参考文献/References:

[1] Mohamad S.Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks[J].Physica D,2001,159(3/4):233-251.
[2]Chen X,Song Q.Global exponential stability of the periodic solution of delayed Cohen-Grossberg neural networks with discontinuous activations[J].Neurocomputing,2010,73(16/18):3 097-3 104.
[3]Chen A,Huang L,Cao J.Existence and stability of almost periodic solution for BAM neural networks with delays[J].Applied Mathematics and Computation,2003,137(1):177-193.
[4]Hahnloser R.On the piecewise analysis of networks of linear hreshold neurons[J].Neural Networks,1998,11(4):691-697.
[5]Forti M,Nistri P.Global convergence of neural networks with discontinuous neuron activations[J].IEEE Transactions on Circuits and Systems Ⅰ,2003,50(11):1 421-1 435.
[6]Cheng C Y,Lin K H,Shih C W.Multistability and convergence in delayed neural networks[J].Physica D,2007,225(1):61-74.
[7]Huang G,Cao J.Multistability in bidirectional associative memory neural networks[J].Physics Letters A,2008,372(16):2 842-2 854.
[8]Shih C W,Tseng J P.Convergent dynamics for multistable delayed neural networks[J].Nonlinearity,2008,21(10):2 361-2 389.
[9]Nie X,Cao J.Multistability of competitive neural networks with time-varying and distributed delays[J].Nonlinear Analysis:Real World Applications,2009,10(2):928-942.
[10]Huang G,Cao J.Delay-dependent multistability in recurrent neural networks[J].Neural Networks,2010,23(2):201-209.
[11]Zhang L,Yi Z,Yu H,et al.Some multistability properties of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions[J].Neurocomputing,2009,72(16/18):3 809-3 817.
[12]Huang Z,Song Q,Feng C.Multistability in networks with self-excitation and high-order synaptic connectivity[J].IEEE Transactions on Circuits and Systems Ⅰ,2010,57(8):2 144-2 155.
[13]Nie X,Huang Z.Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions[J].Neurocomputing,2012,82(1):1-13.

相似文献/References:

[1]陈书谦,柏桂枝.基于神经网络的火焰燃烧稳定性算法研究[J].南京师大学报(自然科学版),2012,35(04):140.
 Chen Shuqian,Bai Guizhi.Research on Flame Combustion Stability Based on Neural Network[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(03):140.
[2]叶聪,沈金龙.一种显著性区域提取的新方法[J].南京师大学报(自然科学版),2012,35(03):134.
 Ye Cong,Shen Jinlong.A Novel Saliency Region Detection Algorithm[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(03):134.
[3]戚小莎,曾 静,吉根林.双交叉注意力自编码器改进视频异常检测[J].南京师大学报(自然科学版),2023,46(01):110.[doi:10.3969/j.issn.1001-4616.2023.01.015]
 Qi Xiaosha,Zeng Jing,Ji Genlin.Improved Video Anomaly Detection with Dual Criss-Cross Attention Auto Encoder[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(03):110.[doi:10.3969/j.issn.1001-4616.2023.01.015]
[4]张文娟,张 彬,杨皓哲.基于双注意力机制的成绩预测[J].南京师大学报(自然科学版),2023,46(04):103.[doi:10.3969/j.issn.1001-4616.2023.04.014]
 Zhang Wenjuan,Zhang Bin,Yang Haozhe.Performance Prediction based on Dual-Attention Mechanism[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(03):103.[doi:10.3969/j.issn.1001-4616.2023.04.014]
[5]张大鹏,程学亮,孙明霞.DeephitTM:医学生存分析的时间相关性深度学习模型[J].南京师大学报(自然科学版),2024,(03):138.[doi:10.3969/j.issn.1001-4616.2024.03.017]
 Zhang Dapeng,Cheng Xueliang,Sun Mingxia.DeephitTM:a Time-dependent Deep Learning Model for Medical Survival Analysis[J].Journal of Nanjing Normal University(Natural Science Edition),2024,(03):138.[doi:10.3969/j.issn.1001-4616.2024.03.017]

备注/Memo

备注/Memo:
收稿日期:2012-12-19.
基金项目:国家自然科学基金(61273021、11271389)、重庆市自然科学基金(CSTC2011AC6104、CSTC2011jjA00012、CSTC2010BB27)、重庆市教委科学技术研究项目(KJ120420).
通讯联系人:谭远顺,博士,教授,研究方向:常微分方程与动力系统.E-mail:tanys@cqjtu.edu.cn
更新日期/Last Update: 2013-09-30