Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays

This paper deals with the problem of global exponential synchronization of a class of memristor-based recurrent neural networks with time-varying delays based on the fuzzy theory and Lyapunov method. First, a memristor-based recurrent neural network is designed. Then, considering the state-dependent properties of the memristor, a new fuzzy model employing parallel distributed compensation (PDC) gives a new way to analyze the complicated memristor-based neural networks with only two subsystems. Comparisons between results in this paper and in the previous ones have been made. They show that the results in this paper improve and generalized the results derived in the previous literature. An example is also given to illustrate the effectiveness of the results.

[1]  Pagavathigounder Balasubramaniam,et al.  Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays , 2012 .

[2]  Mohammad Javad Sharifi,et al.  General SPICE Models for Memristor and Application to Circuit Simulation of Memristor-Based Synapses and Memory Cells , 2010, J. Circuits Syst. Comput..

[3]  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.

[4]  Neyir Ozcan,et al.  Global robust stability analysis of neural networks with multiple time delays , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Zhigang Zeng,et al.  Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[6]  Dharmendra S. Modha,et al.  The cat is out of the bag: cortical simulations with 109 neurons, 1013 synapses , 2009, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis.

[7]  Zhigang Zeng,et al.  Dynamics Analysis of a Class of Memristor-Based Recurrent Networks with Time-Varying Delays in the Presence of Strong External Stimuli , 2011, Neural Processing Letters.

[8]  Jinde Cao,et al.  An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks , 2002 .

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

[10]  Z. Zeng,et al.  Adaptive synchronization of memristor-based Chuaʼs circuits , 2012 .

[11]  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.

[12]  Jigen Peng,et al.  Exponential lag synchronization of fuzzy cellular neural networks with time-varying delays , 2012, J. Frankl. Inst..

[13]  Giacomo Indiveri,et al.  A neuromorphic VLSI device for implementing 2D selective attention systems , 2001, IEEE Trans. Neural Networks.

[14]  Qing Zhu,et al.  New results of global robust exponential stability of neural networks with delays , 2010 .

[15]  Bertram E. Shi,et al.  An ON-OFF orientation selective address event representation image transceiver chip , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Shih-Yu Li,et al.  Fuzzy Modeling and Synchronization of Two Totally Different Chaotic Systems via Novel Fuzzy Model , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Chian-Song Chiu,et al.  Robust Output Regulation of T--S Fuzzy Systems With Multiple Time-Varying State and Input Delays , 2009, IEEE Transactions on Fuzzy Systems.

[19]  Qing Zhu,et al.  Design of exponential state estimator for neural networks with distributed delays , 2009 .

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

[21]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[22]  Yong Tan,et al.  Harmless delays for global exponential stability of Cohen-Grossberg neural networks , 2007, Math. Comput. Simul..

[23]  Youyi Wang,et al.  Control Synthesis of Continuous-Time T-S Fuzzy Systems With Local Nonlinear Models , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  Sabri Arik,et al.  A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks , 2013, Neural Networks.

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

[26]  Jinde Cao,et al.  Global exponential stability results for neutral-type impulsive neural networks , 2010 .

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

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

[29]  S. Zhong,et al.  T-S fuzzy model-based impulsive control of chaotic systems with exponential decay rate , 2007 .

[30]  Zhigang Zeng,et al.  Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type , 2012, Neural Networks.

[31]  Jinde Cao,et al.  Global Synchronization in an Array of Delayed Neural Networks With Hybrid Coupling , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[32]  B. Cui,et al.  Global robust exponential stability of delayed neural networks , 2008 .

[33]  S. Arik.  Global robust stability analysis of neural networks with discrete time delays , 2005 .

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

[35]  Ting Wang,et al.  Exponential synchronization for delayed chaotic neural networks with nonlinear hybrid coupling , 2012, Neurocomputing.

[36]  Ju H. Park,et al.  Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay , 2012, Appl. Math. Comput..

[37]  Wei Yang Lu,et al.  Nanoscale memristor device as synapse in neuromorphic systems. , 2010, Nano letters.

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

[39]  Albert Y. Zomaya.  Handbook of Nature-Inspired and Innovative Computing - Integrating Classical Models with Emerging Technologies , 2006 .

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

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

[42]  J. Suehle,et al.  A Flexible Solution-Processed Memristor , 2009, IEEE Electron Device Letters.

[43]  Sabri Arik,et al.  New results for robust stability of dynamical neural networks with discrete time delays , 2010, Expert Syst. Appl..

[44]  Young-Wan Cho,et al.  T-S model based indirect adaptive fuzzy control using online parameter estimation , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[45]  Shih-Chii Liu,et al.  Temporal coding in a silicon network of integrate-and-fire neurons , 2004, IEEE Transactions on Neural Networks.