Pinning synchronization of delayed neural networks.

This paper investigates adaptive pinning synchronization of a general weighted neural network with coupling delay. Unlike recent works on pinning synchronization which proposed the possibility that synchronization can be reached by controlling only a small fraction of neurons, this paper aims to answer the following question: Which neurons should be controlled to synchronize a neural network? By using Schur complement and Lyapunov function methods, it is proved that under a mild topology-based condition, some simple adaptive feedback controllers are sufficient to globally synchronize a general delayed neural network. Moreover, for a concrete neurobiological network consisting of identical Hindmarsh-Rose neurons, a specific pinning control technique is introduced and some numerical examples are presented to verify our theoretical results.

[1]  J. Rogers.  Chaos , 1876, Molecular Vibrations.

[2]  Sanjit K. Mitra,et al.  Kronecker Products, Unitary Matrices and Signal Processing Applications , 1989, SIAM Rev..

[3]  Hiroshi Nozawa,et al.  A neural network model as a globally coupled map and applications based on chaos. , 1992, Chaos.

[4]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[5]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[6]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[7]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[8]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[9]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[10]  Antonino Raffone,et al.  Dynamic synchronization and chaos in an associative neural network with multiple active memories. , 2003, Chaos.

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

[12]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[13]  Martin Hasler,et al.  Synchronization of bursting neurons: what matters in the network topology. , 2005, Physical review letters.

[14]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[15]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[16]  Jinde Cao,et al.  Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks. , 2006, Chaos.

[17]  Yi-You Hou,et al.  Stability analysis of neural networks with interval time-varying delays. , 2007, Chaos.

[18]  Jinde Cao,et al.  An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural network via nonsmooth analysis , 2007, Neural Networks.

[19]  Mario di Bernardo,et al.  Effects of Degree Correlation on the Synchronization of Networks of oscillators , 2007, Int. J. Bifurc. Chaos.

[20]  F. Garofalo,et al.  Controllability of complex networks via pinning. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

[22]  Xiaoqun Wu.  Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay , 2008 .

[23]  E. Ott,et al.  Adaptive synchronization of dynamics on evolving complex networks. , 2008, Physical review letters.

[24]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..