New results on exponential synchronization of memristor-based neural networks with discontinuous neuron activations

This paper investigates the exponential synchronization of delayed memristor-based neural networks (MNNs) with discontinuous activation functions. Based on the framework of Filippov solution and differential inclusion theory, using new analytical techniques and introducing suitable Lyapunov functionals, some novel sufficient conditions ensuring the exponential synchronization of considered networks are established via two types of discontinuous controls: linear feedback control and adaptive control. In particular, we extend the discontinuous control strategies for neural networks with continuous dynamics to MNNs with discontinuous activations. Numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized MNN circuits involving discontinuous activations and time-varying delays.

[1]  Z. Njitacke Tabekoueng,et al.  Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit. , 2015, Chaos.

[2]  Guodong Zhang,et al.  Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control , 2014, Neural Networks.

[3]  Lian Duan,et al.  Global dissipativity of mixed time-varying delayed neural networks with discontinuous activations , 2014, Commun. Nonlinear Sci. Numer. Simul..

[4]  Lihong Huang,et al.  Global asymptotic stability of delayed neural networks with discontinuous neuron activations , 2009, Neurocomputing.

[5]  Yu. S. Ledyaev,et al.  Nonsmooth analysis and control theory , 1998 .

[6]  Jinde Cao,et al.  Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach , 2014, Neural Networks.

[7]  Matthew D. Pickett,et al.  SPICE modeling of memristors , 2011, 2011 IEEE International Symposium of Circuits and Systems (ISCAS).

[8]  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.

[9]  Quan Yin,et al.  Adaptive Synchronization of Memristor-Based Neural Networks with Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

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

[11]  J. Yang,et al.  Switching dynamics in titanium dioxide memristive devices , 2009 .

[12]  Jinde Cao,et al.  Complete Periodic Synchronization of Delayed Neural Networks with Discontinuous Activations , 2010, Int. J. Bifurc. Chaos.

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

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

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

[16]  Lihong Huang,et al.  Global convergence of periodic solution of neural networks with discontinuous activation functions , 2009 .

[17]  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.

[18]  Duccio Papini,et al.  Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations , 2005 .

[19]  Lixiang Li,et al.  Synchronization control of memristor-based recurrent neural networks with perturbations , 2014, Neural Networks.

[20]  Bo Liu,et al.  New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides , 2012, Neural Networks.

[21]  S. Sastry,et al.  A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators , 1987 .

[22]  Peng Li,et al.  Dynamical Properties and Design Analysis for Nonvolatile Memristor Memories , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  Zhidong Teng,et al.  Exponential lag synchronization for memristor-based neural networks with mixed time delays via hybrid switching control , 2016, J. Frankl. Inst..

[24]  Zhidong Teng,et al.  Finite-time synchronization for memristor-based neural networks with time-varying delays , 2015, Neural Networks.

[25]  Wei Zhang,et al.  Synchronization of Memristor-Based Coupling Recurrent Neural Networks With Time-Varying Delays and Impulses , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[26]  M. Forti,et al.  Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations , 2006 .

[27]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[28]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[29]  R. Williams,et al.  How We Found The Missing Memristor , 2008, IEEE Spectrum.

[30]  Shukai Duan,et al.  Memristor Model and its Application for Chaos Generation , 2012, Int. J. Bifurc. Chaos.

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

[32]  Massimiliano Di Ventra,et al.  Experimental demonstration of associative memory with memristive neural networks , 2009, Neural Networks.

[33]  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.

[34]  Leon O. Chua,et al.  Memristor Bridge Synapses , 2012, Proceedings of the IEEE.

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

[36]  Jinde Cao,et al.  Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches , 2011, Neural Networks.

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

[38]  Sarah K. Spurgeon,et al.  Sliding mode observers for fault detection and isolation , 2000, Autom..

[39]  Zhigang Zeng,et al.  Event-based control for memristive systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

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

[41]  Bharathwaj Muthuswamy,et al.  Memristor-Based Chaotic Circuits , 2009 .

[42]  Zhigang Zeng,et al.  Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays , 2013, Neural Networks.