Global Synchronization Criteria of Linearly Coupled Neural Network Systems With Time-Varying Coupling

In this paper, global synchronization of linearly coupled neural network (NN) systems with time-varying coupling is investigated. The dynamical behavior of the uncoupled system at each node is general, which can be chaotic or others; the coupling configuration is time varying, i.e., the coupling matrix is not a constant matrix. Based on Lyapunov function method and the specific property of Householder transform, some criteria for the global synchronization are obtained. By these criteria, one can verify whether the coupled system with time-varying coupling is globally synchronized, which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration. Finally, two simulations are given to demonstrate the effectiveness of the theoretical results.

[1]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2005, IEEE Transactions on Automatic Control.

[2]  J. Kurths,et al.  Network synchronization, diffusion, and the paradox of heterogeneity. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Liang Zhao,et al.  A network of dynamically coupled chaotic maps for scene segmentation , 2001, IEEE Trans. Neural Networks.

[4]  DeLiang Wang,et al.  Synchronization and desynchronization in a network of locally coupled Wilson-Cowan oscillators , 1996, IEEE Trans. Neural Networks.

[5]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[6]  DeLiang Wang,et al.  Emergent synchrony in locally coupled neural oscillators , 1995, IEEE Trans. Neural Networks.

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

[8]  Adilson E Motter,et al.  Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? , 2003, Physical review letters.

[9]  T. Carroll,et al.  MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS , 1999 .

[10]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[11]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[12]  C. Wu.  Synchronization in networks of nonlinear dynamical systems coupled via a directed graph , 2005 .

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

[14]  M Chavez,et al.  Synchronization in complex networks with age ordering. , 2005, Physical review letters.

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

[16]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[17]  H. Nijmeijer,et al.  Cooperative oscillatory behavior of mutually coupled dynamical systems , 2001 .

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

[19]  R. Schwarzenberger.  ORDINARY DIFFERENTIAL EQUATIONS , 1982 .

[20]  P. Hartman.  Ordinary Differential Equations , 1965 .

[21]  F. Zou,et al.  Bifurcation and chaos in cellular neural networks , 1993 .

[22]  L. Chua,et al.  COEXISTENCE OF LOW- AND HIGH-DIMENSIONAL SPATIOTEMPORAL CHAOS IN A CHAIN OF DISSIPATIVELY COUPLED CHUA’S CIRCUITS , 1994 .

[23]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[24]  Louis M. Pecora,et al.  Synchronization stability in Coupled oscillator Arrays: Solution for Arbitrary Configurations , 2000, Int. J. Bifurc. Chaos.

[25]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[26]  S. Boccaletti,et al.  Synchronization is enhanced in weighted complex networks. , 2005, Physical review letters.

[27]  Leon O. Chua,et al.  Spiral waves on a 2-D array of nonlinear circuits , 1993 .

[28]  Jean-Jacques E. Slotine,et al.  Contraction analysis of time-delayed communications and group cooperation , 2006, IEEE Transactions on Automatic Control.

[29]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .