Complex projective synchronization in drive-response stochastic coupled networks with complex-variable systems and coupling time delays

Abstract In this paper, the complex projective synchronization in drive-response stochastic coupled networks with complex-variable systems and linear coupling time delays are considered. The pinning control scheme are adopted to achieve complex projective synchronization and several simple and practical sufficient conditions are obtained in a general drive-response network. In addition, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical simulations are provided to show the effectiveness and feasibility of the proposed methods.

[1]  Yong He,et al.  Exponential synchronization of neural networks with time-varying mixed delays and sampled-data , 2010, Neurocomputing.

[2]  Damon Centola,et al.  The Spread of Behavior in an Online Social Network Experiment , 2010, Science.

[3]  J Kurths,et al.  Transition from phase to generalized synchronization in time-delay systems. , 2008, Chaos.

[4]  Liu Jin-Gui.  Generalized projective synchronization of fractional-order complex networks with nonidentical nodes , 2012 .

[5]  Hongtao Lu,et al.  Generalized projective synchronization between two different general complex dynamical networks with delayed coupling , 2010 .

[6]  C. T. Butts,et al.  Revisiting the Foundations of Network Analysis , 2009, Science.

[7]  Wei Wu,et al.  Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  M. Feinberg,et al.  Structural Sources of Robustness in Biochemical Reaction Networks , 2010, Science.

[9]  Dibakar Ghosh,et al.  Linear observer based projective synchronization in delay Rössler system , 2010 .

[10]  Xinchu Fu,et al.  Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems , 2013 .

[11]  Peng Shi,et al.  Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control , 2013 .

[12]  Jian Xu,et al.  Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller , 2010, Appl. Math. Comput..

[13]  Choon Ki Ahn,et al.  Anti-synchronization of Time-delayed Chaotic Neural Networks Based on Adaptive Control , 2009 .

[14]  Licheng Jiao,et al.  Projective synchronization with different scale factors in a driven–response complex network and its application in image encryption , 2010 .

[15]  W. Kinzel,et al.  Synchronization of unidirectional time delay chaotic networks and the greatest common divisor , 2010, 1012.0990.

[16]  Tianping Chen,et al.  Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling , 2007 .

[17]  Choon Ki Ahn,et al.  Adaptive H∞ Anti-Synchronization for Time-Delayed Chaotic Neural Networks , 2009 .

[18]  Jinde Cao,et al.  Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays , 2011 .

[19]  Rui Xu,et al.  Synchronization of chaotic neural networks with mixed time delays , 2011 .

[20]  Christian Perret,et al.  The stability of numerical simulations of complex stochastic differential equations , 2010 .

[21]  Qinghua Ma,et al.  Mixed outer synchronization of coupled complex networks with time-varying coupling delay. , 2011, Chaos.

[22]  Dibakar Ghosh,et al.  Generalized projective synchronization in time-delayed systems: nonlinear observer approach. , 2009, Chaos.

[23]  Albert-László Barabási,et al.  Scale-Free Networks: A Decade and Beyond , 2009, Science.

[24]  X. Mao,et al.  A note on the LaSalle-type theorems for stochastic differential delay equations , 2002 .

[25]  Shih-Yu Li,et al.  Temporary lag and anticipated synchronization and anti-synchronization of uncoupled time-delayed chaotic systems , 2008 .

[26]  Hong-Xing Yao,et al.  Cluster projective synchronization of complex networks with nonidentical dynamical nodes , 2012 .

[27]  K. Sudheer,et al.  Adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler system , 2011 .

[28]  Xuerong Mao,et al.  Robust stability and controllability of stochastic differential delay equations with Markovian switching , 2004, Autom..

[29]  Santo Banerjee,et al.  Generalized and projective synchronization in modulated time-delayed systems , 2010 .

[30]  Ramakrishna Ramaswamy,et al.  The effect of time-delay on anomalous phase synchronization , 2008 .

[31]  Xinchu Fu,et al.  Complex projective synchronization in coupled chaotic complex dynamical systems , 2012 .

[32]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..