|Table of Contents|

Multistability of Neural Networks With Discontinuous Activation Functions(PDF)

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

Issue:
2013年03期
Page:
16-20
Research Field:
数学
Publishing date:

Info

Title:
Multistability of Neural Networks With Discontinuous Activation Functions
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)
Keywords:
neural networksmultistabilityexponential stabilitydiscontinuous activation functions
PACS:
O175.13
DOI:
-
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.

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.

Memo

Memo:
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Last Update: 2013-09-30