New Algebraic Criteria for Synchronization Stability of Chaotic Memristive Neural Networks With Time-Varying Delays

In this brief, we consider the exponential synchronization of chaotic memristive neural networks with time-varying delays using the Lyapunov functional method and inequality technique. The dynamic analysis here employs the theory of differential equations with discontinuous right-hand side as introduced by Filippov. The designing laws in the synchronization of neural networks are proposed via state or output coupling. In addition, the new proposed algebraic criteria are very easy to verify, and they also enrich and improve the earlier publications. Finally, an example is given to show the effectiveness of the obtained results.

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

[2]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[3]  Meifang Dong.  Global exponential stability and existence of periodic solutions of CNNs with delays , 2002 .

[4]  Tianping Chen,et al.  Synchronization of coupled connected neural networks with delays , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[6]  Jun Wang,et al.  Global output convergence of a class of continuous-time recurrent neural networks with time-varying thresholds , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  C. Leeuwen,et al.  Synchronization of chaotic neural networks via output or state coupling , 2006 .

[8]  Jinde Cao,et al.  Stability of Cohen-Grossberg neural networks with time-varying delays , 2007, Neural Networks.

[9]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[10]  Jinde Cao,et al.  Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects , 2007 .

[11]  Kanjian Zhang,et al.  Synchronization control of recurrent neural networks with distributed delays , 2008 .

[12]  Leon O. Chua,et al.  Memristor oscillators , 2008, Int. J. Bifurc. Chaos.

[13]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[14]  D. Stewart,et al.  The missing memristor found , 2009, Nature.

[15]  Meiqin Liu,et al.  Optimal exponential synchronization of general chaotic delayed neural networks: An LMI approach , 2009, Neural Networks.

[16]  Jinde Cao,et al.  Cluster synchronization in an array of hybrid coupled neural networks with delay , 2009, Neural Networks.

[17]  Jun Wang,et al.  Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching , 2009, IEEE Transactions on Neural Networks.

[18]  Zhang Yi,et al.  Activity Invariant Sets and Exponentially Stable Attractors of Linear Threshold Discrete-Time Recurrent Neural Networks , 2009, IEEE Transactions on Automatic Control.

[19]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[20]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[21]  Yong He,et al.  Exponential synchronization of neural networks with time-varying mixed delays and sampled-data , 2010, Neurocomputing.

[22]  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).

[23]  Fernando Corinto,et al.  Nonlinear Dynamics of Memristor Oscillators , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

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

[26]  Zhigang Zeng,et al.  Synchronization control of a class of memristor-based recurrent neural networks , 2012, Inf. Sci..

[27]  Zhigang Zeng,et al.  Anti-synchronization control of a class of memristive recurrent neural networks , 2013, Commun. Nonlinear Sci. Numer. Simul..