Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays

Abstract In real nervous systems and in the implementation of very large-scale integration (VLSI) circuits, noise is unavoidable, which leads to the stochastic model of the memristor-based recurrent neural networks. Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays is studied and some sufficient conditions in terms of inequalities are derived. Numerical examples are given to demonstrate the effectiveness of the proposed stability criteria.

[1]  Jun Wang,et al.  Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[2]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[3]  Rajendran Samidurai,et al.  New delay dependent robust asymptotic stability for uncertain stochastic recurrent neural networks with multiple time varying delays , 2012, J. Frankl. Inst..

[4]  Jinde Cao,et al.  Global robust stability of delayed recurrent neural networks , 2004 .

[5]  L. Chua Memristor-The missing circuit element , 1971 .

[6]  Zidong Wang,et al.  Robust stability for stochastic Hopfield neural networks with time delays , 2006 .

[7]  Ju H. Park,et al.  State estimation of memristor-based recurrent neural networks with time-varying delays based on passivity theory , 2014, Complex..

[8]  Jun Wang,et al.  An Improved Algebraic Criterion for Global Exponential Stability of Recurrent Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[9]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[10]  Jinde Cao,et al.  On global asymptotic stability of recurrent neural networks with time-varying delays , 2003, Appl. Math. Comput..

[11]  Zhigang Zeng,et al.  Passivity analysis of memristor-based recurrent neural networks with time-varying delays , 2013, J. Frankl. Inst..

[12]  Jinde Cao,et al.  Globally exponential stability conditions for cellular neural networks with time-varying delays , 2002, Appl. Math. Comput..

[13]  Zhigang Zeng,et al.  Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays , 2012, Neurocomputing.

[14]  P. Balasubramaniam Existence of solutions of functional stochastic differential inclusions , 2002 .

[15]  Qiankun Song,et al.  Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach , 2008, Neurocomputing.

[16]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[17]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[18]  Jun Wang,et al.  Global exponential stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[19]  Jun Wang,et al.  Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks , 2002, IEEE Trans. Autom. Control..

[20]  Zhigang Zeng,et al.  Dynamic behaviors of memristor-based delayed recurrent networks , 2012, Neural Computing and Applications.

[21]  Daoyi Xu,et al.  Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays , 2011, Neurocomputing.

[22]  Zhigang Zeng,et al.  Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli , 2006, Neural Networks.

[23]  Zhigang Zeng,et al.  Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays , 2012, Neural Networks.

[24]  Qinghua Zhou,et al.  Exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays , 2008, Appl. Math. Comput..

[25]  J. Tour,et al.  Electronics: The fourth element , 2008, Nature.

[26]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[27]  Z. Zeng,et al.  Dynamic behaviors of a class of memristor-based Hopfield networks , 2011 .

[28]  Jinde Cao,et al.  Global exponential stability and periodic solutions of recurrent neural networks with delays , 2002 .

[29]  Zidong Wang,et al.  Exponential stability of uncertain stochastic neural networks with mixed time-delays , 2007 .

[30]  Jinde Cao,et al.  Exponential stability analysis of uncertain stochastic neural networks with multiple delays , 2007 .

[31]  Zhigang Zeng,et al.  Exponential Stabilization of Memristive Neural Networks With Time Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Guodong Zhang,et al.  Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays , 2012, Neurocomputing.

[33]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[34]  Jinde Cao,et al.  Exponential stability analysis of stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed delays , 2011, Neurocomputing.

[35]  Jun Wang,et al.  Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays , 2013, Neural Networks.