On memristor-based impulsive neural networks with time-delay

This paper studies a group of interconnected memristor-based impulsive neural networks (MINNs) with time-delay and its synchronization mechanism. Due to the impulsive and switching mode, interconnected MINNs are mathematically elaborated in the form of impulsive differential inclusions. Based on theories of Lyapunov functions and impulsive differential equations, asymptotic convergence of synchronization is evaluated for the interconnected MINNs, where the relationship of impulse to convergence rate are specified. It is shown that in addition to the Laplacian coupling, the impulse plays an essential role in the pursuit of synchronization. Simulation work is provided to verify the developed theoretical results.

[1]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[2]  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.

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

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

[5]  Xuemin Shen,et al.  On hybrid impulsive and switching systems and application to nonlinear control , 2005, IEEE Transactions on Automatic Control.

[6]  Hai-Tao Zhang,et al.  Input Delay Compensation in Multi-Agent Systems via Piecewise Constant Control , 2016 .

[7]  A. Thomas,et al.  Memristor-based neural networks , 2013 .

[8]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[9]  Guanrong Chen,et al.  On delayed impulsive Hopfield neural networks , 1999, Neural Networks.

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

[11]  J. Martinerie,et al.  The brainweb: Phase synchronization and large-scale integration , 2001, Nature Reviews Neuroscience.

[12]  Guanrong Chen,et al.  Suppressing chaos in a simplest autonomous memristor-based circuit of fractional order by periodic impulses , 2016 .

[13]  Jun Wang,et al.  Global Exponential Synchronization of Multiple Memristive Neural Networks With Time Delay via Nonlinear Coupling , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Gang Feng,et al.  Synchronization of Complex Dynamical Networks With Time-Varying Delays Via Impulsive Distributed Control , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[16]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

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

[18]  L.O. Chua,et al.  Memristive devices and systems , 1976, Proceedings of the IEEE.

[19]  Wei He,et al.  Investigation and Manipulation of Different Analog Behaviors of Memristor as Electronic Synapse for Neuromorphic Applications , 2016, Scientific Reports.

[20]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[21]  M. Benchohra,et al.  Impulsive differential equations and inclusions , 2006 .

[22]  Zhi-Hong Guan,et al.  Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control , 2014, Autom..

[23]  Jan Lunze,et al.  A deterministic gossiping algorithm for the synchronization of multi-agent systems∗ , 2015 .