Pinning synchronization of fractional-order delayed complex networks with non-delayed and delayed couplings

ABSTRACT This paper considers the global synchronization of fractional-order delayed complex networks with non-delayed and delayed couplings based on pinning control. With the help of comparison theorems for fractional-order linear systems with multiple time delays, some novel and useful synchronisation criteria are presented by adding linear error feedback controllers to certain selected nodes. Here, the coupling matrices need not be symmetric or irreducible. What is more, it is shown that the model and results in the paper are more general than those in the literature. A numerical example is given to demonstrate the effectiveness and feasibility of the obtained results.

[1]  Yun Zhang,et al.  Robust projective outer synchronization of coupled uncertain fractional-order complex networks , 2013 .

[2]  Fuzhong Nian,et al.  Optimal pinning synchronization on directed complex network. , 2011, Chaos.

[3]  YI LIANG,et al.  Synchronizability on complex networks via pinning control , 2013 .

[4]  Jinde Cao,et al.  Sampled-Data $$H_{\infty }$$H∞ Synchronization of Chaotic Lur’e Systems with Time Delay , 2015, Circuits Syst. Signal Process..

[5]  Jinde Cao,et al.  Pinning synchronization of coupled inertial delayed neural networks , 2014, Cognitive Neurodynamics.

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

[7]  Xing-yuan Wang,et al.  Projective synchronization of fractional order chaotic system based on linear separation , 2008 .

[8]  Jianwen Feng,et al.  Mixed outer synchronization of two coupled complex networks with time-varying delay coupling and non-delay coupling , 2015 .

[9]  Tiedong Ma,et al.  Cluster synchronization in fractional-order complex dynamical networks , 2012 .

[10]  M. Porfiri,et al.  Node-to-node pinning control of complex networks. , 2009, Chaos.

[11]  Tiedong Ma,et al.  Hybrid synchronization of coupled fractional-order complex networks , 2015, Neurocomputing.

[12]  Jinhu Lü,et al.  Stability analysis of linear fractional differential system with multiple time delays , 2007 .

[13]  Jinde Cao,et al.  Distributed adaptive control of pinning synchronization in complex dynamical networks with non-delayed and delayed coupling , 2015, International Journal of Control, Automation and Systems.

[14]  Yan Zhou,et al.  An indirect Lyapunov approach to the observer-based robust control for fractional-order complex dynamic networks , 2014, Neurocomputing.

[15]  Xue-Zhi Li,et al.  Hopf Bifurcation for a Model of HIV Infection of CD4+ T Cells with Virus Released Delay , 2011 .

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

[17]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[18]  Jinde Cao,et al.  Pinning Synchronization of Delayed Neural Networks with Nonlinear Inner-Coupling , 2011 .

[19]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

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

[21]  A. Alikhanov.  A priori estimates for solutions of boundary value problems for fractional-order equations , 2010, 1105.4592.

[22]  Jürgen Kurths,et al.  Synchronization between two coupled complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Manfeng Hu,et al.  Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control , 2015 .

[24]  Zengrong Liu,et al.  Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control , 2011 .

[25]  Gangquan Si,et al.  Parameter estimation and topology identification of uncertain fractional order complex networks , 2012 .

[26]  Yi Liang,et al.  Adaptive synchronization in complex networks with non-delay and variable delay couplings via pinning control , 2014, Neurocomputing.

[27]  Changpin Li,et al.  Pinning adaptive anti-synchronization between two general complex dynamical networks with non-delayed and delayed coupling , 2012, Applied Mathematics and Computation.

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

[29]  Shengyuan Xu,et al.  Pinning control for cluster synchronisation of complex dynamical networks with semi-Markovian jump topology , 2015, Int. J. Control.

[30]  W. K. Wong,et al.  Robust synchronization of fractional-order complex dynamical networks with parametric uncertainties , 2012 .

[31]  Jing-Wen Yi,et al.  Adaptive pinning cluster synchronization of fractional-order complex dynamical networks , 2014, Appl. Math. Comput..

[32]  Mohammad Saleh Tavazoei,et al.  Robust outer synchronization between two complex networks with fractional order dynamics. , 2011, Chaos.

[33]  Fangfang Zhang,et al.  Complex function projective synchronization of complex chaotic system and its applications in secure communication , 2013, Nonlinear Dynamics.

[34]  Guanrong Chen,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  Song Zheng,et al.  Impulsive synchronization of complex networks with non-delayed and delayed coupling , 2009 .

[36]  Shihua Chen,et al.  Global synchronization of nonlinearly coupled complex networks with non-delayed and delayed coupling , 2010 .

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

[38]  Xingyuan Wang,et al.  Synchronization in complex networks with non-delay and delay couplings via intermittent control with two switched periods , 2014 .

[39]  Jinde Cao,et al.  Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control , 2014, Neurocomputing.

[40]  Guang-Hong Yang,et al.  Adaptive synchronization of a class of nonlinearly coupled complex networks , 2012, 2012 24th Chinese Control and Decision Conference (CCDC).

[41]  Yi Liang,et al.  A method of quickly calculating the number of pinning nodes on pinning synchronization in complex networks , 2014, Appl. Math. Comput..

[42]  Jinde Cao,et al.  On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[43]  Yi Chai,et al.  Adaptive pinning synchronization in fractional-order complex dynamical networks , 2012 .

[44]  Liping Chen,et al.  Comparison principles and stability of nonlinear fractional-order cellular neural networks with multiple time delays , 2015, Neurocomputing.

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

[46]  Hao Shen,et al.  Mixed H∞/passive synchronization for complex dynamical networks with sampled-data control , 2015, Appl. Math. Comput..

[47]  Wu Xiang-Jun,et al.  Outer synchronization between two different fractional-order general complex dynamical networks , 2010 .

[48]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

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

[50]  Xing-yuan Wang,et al.  Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control , 2009 .

[51]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[52]  Jinde Cao,et al.  Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller , 2013, SIAM J. Control. Optim..

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

[54]  Junwei Wang,et al.  Outer Synchronization between Fractional-Order Complex Networks: A Non-Fragile Observer-based Control Scheme , 2013, Entropy.

[55]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .