Synchronization of Interconnected Discontinuous Neural Networks With Nonlinear Coupling Functions

Some criteria on exponential synchronization of multiple identical discontinuous neural networks with time delay are given in this paper. Different from the available results, the nodes of complex networks are coupled via nonlinear discontinuous functions. First, we study the existence of Filippov solution of the nonlinear coupled discontinuous neural networks (NCDNNs) based on differential inclusion theory. In addition, we derive some exponential synchronization criteria of the NCDNNs. Finally, we design a pinning impulsive controller to realize the exponential synchronization of NCDNNs. Numerical examples are presented to illustrate the obtained results.

[1]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[2]  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.

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

[4]  Xinsong Yang,et al.  Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations , 2015, J. Frankl. Inst..

[5]  Wei Wu,et al.  Global Synchronization Criteria of Linearly Coupled Neural Network Systems With Time-Varying Coupling , 2008, IEEE Transactions on Neural Networks.

[6]  Jinde Cao,et al.  Exponential Synchronization of Delayed Neural Networks With Discontinuous Activations , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

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

[9]  Jinde Cao,et al.  Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control , 2017, Neural Networks.

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

[11]  Jinde Cao,et al.  Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control , 2013 .

[12]  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.

[13]  Tianping Chen,et al.  Synchronization of Nonlinear Coupled Networks via Aperiodically Intermittent Pinning Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Jinde Cao,et al.  Robust State Estimation for Neural Networks With Discontinuous Activations , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Zengyun Wang,et al.  Synchronization analysis of linearly coupleddelayed neural networks with discontinuous activations , 2015 .

[16]  J. Aubin,et al.  Existence of Solutions to Differential Inclusions , 1984 .

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

[18]  Lihong Huang,et al.  Periodic synchronization control of discontinuous delayed networks by using extended Filippov-framework , 2015, Neural Networks.

[19]  Jinde Cao,et al.  Finite-time synchronization of complex networks with nonidentical discontinuous nodes , 2013, Nonlinear Dynamics.

[20]  Tianping Chen,et al.  Synchronization of Complex Networks via Aperiodically Intermittent Pinning Control , 2015, IEEE Transactions on Automatic Control.

[21]  Lihong Huang,et al.  LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations , 2009, Appl. Math. Comput..

[22]  Jinde Cao,et al.  Nonsmooth finite-time stabilization of neural networks with discontinuous activations , 2014, Neural Networks.

[23]  W. Marsden.  I and J , 2012 .

[24]  Kexue Zhang,et al.  Pinning Impulsive Synchronization of Reaction–Diffusion Neural Networks With Time-Varying Delays , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Chuandong Li,et al.  Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[26]  Zhenyuan Guo,et al.  Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control , 2016, Neural Networks.

[27]  Tianping Chen,et al.  Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions , 2006 .

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

[29]  Jinde Cao,et al.  Multistability of neural networks with discontinuous activation function , 2008 .

[30]  Jun Wang,et al.  Robust Synchronization of Multiple Memristive Neural Networks With Uncertain Parameters via Nonlinear Coupling , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[31]  Lihong Huang,et al.  Finite-time stabilization control for discontinuous time-delayed networks: New switching design , 2016, Neural Networks.

[32]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[33]  Lihong Huang,et al.  Generalized Lyapunov method for discontinuous systems , 2009 .

[34]  Tianping Chen,et al.  Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions , 2006, Neural Computation.

[35]  Xinsong Yang,et al.  Synchronization of uncertain hybrid switching and impulsive complex networks , 2018, Applied Mathematical Modelling.

[36]  Zhenyuan Guo,et al.  Global Synchronization of Multiple Recurrent Neural Networks With Time Delays via Impulsive Interactions , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Qingshan Liu,et al.  A Collective Neurodynamic Approach to Distributed Constrained Optimization , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[38]  Lihong Huang,et al.  Synchronization analysis of networks with both delayed and non-delayed couplings via adaptive pinning control method ☆ , 2010 .

[39]  Yin Sheng,et al.  Finite-time robust stabilization of uncertain delayed neural networks with discontinuous activations via delayed feedback control , 2016, Neural Networks.

[40]  Kexue Zhang,et al.  Synchronization of linear dynamical networks on time scales: Pinning control via delayed impulses , 2016, Autom..

[41]  Frank C. Hoppensteadt,et al.  Pattern recognition via synchronization in phase-locked loop neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[42]  Jinde Cao,et al.  Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays , 2004, Neural Networks.

[43]  Jinde Cao,et al.  Event-Triggered Schemes on Leader-Following Consensus of General Linear Multiagent Systems Under Different Topologies , 2017, IEEE Transactions on Cybernetics.