Lag Synchronization Criteria for Memristor-Based Coupled Neural Networks via Parameter Mismatches Analysis Approach

This letter focuses on lag synchronization control analysis for memristor-based coupled neural networks with parameter mismatches. Due to the parameter mismatches, lag complete synchronization in general cannot be achieved. First, based on the -measure method, generalized Halanay inequality, together with control algorithms, some sufficient conditions are obtained to ensure that coupled memristor-based neural networks are in a state of lag synchronization with an error. Moreover, the error level is estimated. Second, we show that memristor-based coupled neural networks with parameter mismatches can reach lag complete synchronization under a discontinuous controller. Finally, two examples are given to illustrate the effectiveness of the proposed criteria and well support theoretical results.

[1]  Daniel W. C. Ho,et al.  Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach , 2016, IEEE Transactions on Cybernetics.

[2]  Guodong Zhang,et al.  Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays , 2013, Neural Networks.

[3]  Leimin Wang,et al.  Finite-Time Stabilizability and Instabilizability of Delayed Memristive Neural Networks With Nonlinear Discontinuous Controller , 2015, IEEE Transactions on Neural Networks and Learning Systems.

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

[5]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[6]  Zhigang Zeng,et al.  Circuit design and exponential stabilization of memristive neural networks , 2015, Neural Networks.

[7]  Zhigang Zeng,et al.  Exponential Adaptive Lag Synchronization of Memristive Neural Networks via Fuzzy Method and Applications in Pseudorandom Number Generators , 2014, IEEE Transactions on Fuzzy Systems.

[8]  Leon O. Chua,et al.  Memristor Bridge Synapse-Based Neural Network and Its Learning , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Wei Zhang,et al.  Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control , 2016, Neurocomputing.

[10]  Jinde Cao,et al.  Lag Quasi-Synchronization of Coupled Delayed Systems With Parameter Mismatch , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Jinde Cao,et al.  Exponential synchronization of chaotic neural networks: a matrix measure approach , 2009 .

[12]  Zhigang Zeng,et al.  Multistability of periodic delayed recurrent neural network with memristors , 2012, Neural Computing and Applications.

[13]  Jun Wang,et al.  Global Exponential Synchronization of Two Memristor-Based Recurrent Neural Networks With Time Delays via Static or Dynamic Coupling , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[14]  Guodong Zhang,et al.  Passivity analysis for memristor-based recurrent neural networks with discrete and distributed delays. , 2015, Neural networks : the official journal of the International Neural Network Society.

[15]  Leon O. Chua,et al.  A Circuit-Based Learning Architecture for Multilayer Neural Networks With Memristor Bridge Synapses , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[17]  Haijun Jiang,et al.  Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays , 2015, Cognitive Neurodynamics.

[18]  Chuandong Li,et al.  Estimation on Error Bound of Lag Synchronization of Chaotic Systems with Time Delay and Parameter Mismatch , 2010 .

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

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

[21]  Frank Z. Wang,et al.  Delayed switching applied to memristor neural networks , 2012 .

[22]  Jinde Cao,et al.  Finite-time synchronization of fractional-order memristor-based neural networks with time delays , 2016, Neural Networks.

[23]  Liping Wen,et al.  Generalized Halanay inequalities for dissipativity of Volterra functional differential equations , 2008 .

[24]  Jinde Cao,et al.  Intermittent control on switched networks via $${\varvec{\omega }}$$ω-matrix measure method , 2014 .

[25]  Jinde Cao,et al.  Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays , 2015, Appl. Math. Comput..

[26]  Jinde Cao,et al.  Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays , 2014, Cognitive Neurodynamics.

[27]  Jinde Cao,et al.  Estimation on Domain of Attraction and Convergence Rate of Hopfield Continuous Feedback Neural Networks , 2001, J. Comput. Syst. Sci..

[28]  Jun Wang,et al.  Attractivity Analysis of Memristor-Based Cellular Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Ronald Tetzlaff,et al.  Synchronization conditions in simple memristor neural networks , 2015, J. Frankl. Inst..