Partial-information-based synchronization analysis for complex dynamical networks

Abstract The model of complex dynamical networks with partial information transmission is introduced. Unlike existing complex network models, the information transmission between the nodes is assumed to have an imperfect physical condition — only partial information can be transmitted. Furthermore, for varying connections, the partly transmitted information can be completely distinct. This communication constraint makes the network harder to achieve synchronization. To reflect a more practical situation, we consider the complex networks with two typical kinds of inner coupling matrix: diagonal matrix and lower triangle matrix. By using an efficient decomposition method, some synchronization criteria are then derived for the complex networks with partial information transmission. Finally, a complex network with chaotic dynamics is constructed as an example to illustrate the effectiveness of the proposed results.

[1]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.

[2]  Jianbin Qiu,et al.  Observer-Based Piecewise Affine Output Feedback Controller Synthesis of Continuous-Time T–S Fuzzy Affine Dynamic Systems Using Quantized Measurements , 2012, IEEE Transactions on Fuzzy Systems.

[3]  J. Kurths,et al.  Structure–function relationship in complex brain networks expressed by hierarchical synchronization , 2007 .

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

[5]  JIANQUAN LU,et al.  Synchronization in an Array of Nonlinearly Coupled Chaotic Neural Networks with Delay Coupling , 2008, Int. J. Bifurc. Chaos.

[6]  Babak Hassibi,et al.  On the capacity of MIMO broadcast channels with partial side information , 2005, IEEE Transactions on Information Theory.

[7]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  Edward Ott,et al.  Characterizing the dynamical importance of network nodes and links. , 2006, Physical review letters.

[9]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Potsdam,et al.  Complex networks in climate dynamics. Comparing linear and nonlinear network construction methods , 2009, 0907.4359.

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

[12]  Jinde Cao,et al.  Adaptive synchronization in tree-like dynamical networks , 2007 .

[13]  Huijun Gao,et al.  Pinning Distributed Synchronization of Stochastic Dynamical Networks: A Mixed Optimization Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Rahul Jain,et al.  Geographical routing using partial information for wireless ad hoc networks , 2001, IEEE Wirel. Commun..

[15]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[16]  Jianbin Qiu,et al.  Fuzzy-Model-Based Piecewise ${\mathscr H}_{\infty }$ Static-Output-Feedback Controller Design for Networked Nonlinear Systems , 2010, IEEE Transactions on Fuzzy Systems.

[17]  Guanrong Chen,et al.  New criteria for synchronization stability of general complex dynamical networks with coupling delays , 2006 .

[18]  Zidong Wang,et al.  Pinning control of fractional-order weighted complex networks. , 2009, Chaos.

[19]  D. Ho,et al.  Stabilization of complex dynamical networks with noise disturbance under performance constraint , 2011 .

[20]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[21]  Peng Shi,et al.  Exponential Synchronization of Neural Networks With Discrete and Distributed Delays Under Time-Varying Sampling , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[23]  Daniel W. C. Ho,et al.  Synchronization analysis of a complex network family , 2010 .

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

[25]  J. Kurths,et al.  Single impulsive controller for globally exponential synchronization of dynamical networks , 2013 .

[26]  Daniel W. C. Ho,et al.  Globally Exponential Synchronization and Synchronizability for General Dynamical Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[27]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[28]  Changsong Zhou,et al.  Dynamics in Complex Systems , 2009, European Review.

[29]  Jinde Cao,et al.  Synchronization of Markovian Coupled Neural Networks With Nonidentical Node-Delays and Random Coupling Strengths , 2012, IEEE Transactions on Neural Networks and Learning Systems.

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

[31]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[32]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.

[33]  Zidong Wang,et al.  Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling , 2012, IEEE Transactions on Automatic Control.

[34]  Changsong Zhou,et al.  Hierarchical organization unveiled by functional connectivity in complex brain networks. , 2006, Physical review letters.

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

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

[37]  Jinde Cao,et al.  Pinning impulsive stabilization of nonlinear Dynamical Networks with Time-Varying Delay , 2012, Int. J. Bifurc. Chaos.

[38]  M. Young,et al.  The architecture of visual cortex and inferential processes in vision. , 2000, Spatial vision.

[39]  Georgios B. Giannakis,et al.  Adaptive MIMO-OFDM based on partial channel state information , 2004, IEEE Transactions on Signal Processing.

[40]  Huijun Gao,et al.  Distributed Robust Synchronization of Dynamical Networks With Stochastic Coupling , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[42]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Complex Networks With Uncertain Inner Coupling and Incomplete Measurements , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Huijun Gao,et al.  Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings , 2013, IEEE Transactions on Cybernetics.

[44]  Yan-Wu Wang,et al.  Synchronization of Continuous Dynamical Networks With Discrete-Time Communications , 2011, IEEE Transactions on Neural Networks.

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