Journal of Guangxi Normal University(Natural Science Edition) ›› 2011, Vol. 29 ›› Issue (1): 29-34.

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Periodic Oscillation Analysis for a Recurrent Neural NetworksModel with Time Delays

ZHAO Hui-wei1, LI Wen-hua1, FENG Chun-hua1, LUO Xiao-shu2   

  1. 1.College of Mathematical Science,Guangxi Normal University,Guilin Guangxi 541004,China;
    2.College of Electronic Engineering,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2010-10-16 Published:2018-11-16

Abstract: The existence of periodic oscillationsfor a five-neuron recurrent neural network with time delay between neural interconnections is investigated.New criteria are proposed to guarantee the existenceof periodic oscillations for network model.Numerical simulation validates thismethod and demonstrates the correctness of theoretical analysis.

Key words: recurrent neural networks, dealys, periodic oscillation, LMI

CLC Number: 

  • O175.1
[1] RUIZ A,OWENS D H,TOWNLEY S.Existence,learning,and replication of periodic motion in recurrent neural networks[J].IEEE Transactions on Neural Networks,1998,9(4):651-661.
[2] TOWNLEY S,ILCHMANN A,WEISSM G,et al.Existence and learning of oscillations in recurrent neural networks[J].IEEE Transactions on Neural Networks,2000,11(1):205-214.
[3] BéLAIR J,CAMPBELL S A,van den DRIESSCHE P.Frustration stabilityand delay-induced oscillations in a neural network model[J].SIAM J Appl Math,1996,56(1):245-255.
[4] YU Wen-wu,CAO Jin-de.Stability and Hopf bifurcations on a two-neuron system with time delay in the frequency domain[J].Int J Bifur Chaos,2007,17(4):1355-1366.
[5] FENG C,PLAMONDON R.Existence of oscillations in recurrent neuralnetworks with time delay models[J].DCDIS A Suppl Adv Neural Networks,2007,14(S1):111-118.
[6] GAO B,ZHANG Wei-nian.Equilibria and their bifurcations in a recurrent neural network involving iterates of a transcendental function[J].IEEETransactions on Neural Networks,2008,19(5):782-794.
[7] FENG Chun-hua,O'REILLY C,PLAMONDON R.Permanent oscillations in a3-node recurrent neural network model[J].Neurocomputing,2010,74(1/3):274-283.
[8] HALE J.Theory of functional differential equations[M].New York:Springer-Verlag,1977:21-24.
[9] FORTI M,TESI A.New conditions for global stability of neural networks with application to linear and quadratic programming problems[J].IEEE Transactions on Circuits and Systems Ⅰ:Fundamental Theory and Applications,1995,42(7):354-366.
[10] CHAFEE N.A bifurcation problem for a functional differential equation of finitely retarded type[J].Journal of Mathematical Analysis and Applications,1971,35(2):312-348.
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