Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control

In this Letter, time-delay has been introduced in to split the networks, upon which a model of complex dynamical networks with multi-links has been constructed. Moreover, based on Lyapunov stability theory and some hypotheses, we achieve synchronization between two complex networks with different structures by designing effective controllers. The validity of the results was proved through numerical simulations of this Letter.

[1]  Guanrong Chen,et al.  Robust adaptive synchronization of uncertain dynamical networks , 2004 .

[2]  Edgar N. Sánchez,et al.  Chaos control and synchronization, with input saturation, via recurrent neural networks , 2003, Neural Networks.

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

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

[5]  John Scott.  What is social network analysis , 2010 .

[6]  Johnson,et al.  Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Edward Ott,et al.  Large coupled oscillator systems with heterogeneous interaction delays. , 2009, Physical review letters.

[8]  Yamir Moreno,et al.  Synchronization of Kuramoto oscillators in scale-free networks , 2004 .

[9]  Mario di Bernardo,et al.  Adaptive synchronization of complex networks , 2008, Int. J. Comput. Math..

[10]  Beom Jun Kim,et al.  Synchronization on small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Beom Jun Kim,et al.  Factors that predict better synchronizability on complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Albert-László Barabási,et al.  Linked: The New Science of Networks , 2002 .

[13]  C Masoller,et al.  Random delays and the synchronization of chaotic maps. , 2005, Physical review letters.

[14]  E. Ott,et al.  Network synchronization of groups. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[16]  D. Watts.  The “New” Science of Networks , 2004 .

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

[18]  Hans J Herrmann,et al.  Coherence in scale-free networks of chaotic maps. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

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

[21]  J. Kurths,et al.  Enhancing complex-network synchronization , 2004, cond-mat/0406207.

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

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

[24]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[25]  Xiang Li,et al.  On synchronous preference of complex dynamical networks , 2005 .

[26]  R Sevilla-Escoboza,et al.  Experimental approach to the study of complex network synchronization using a single oscillator. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  M. Komuro.  Birth and death of the double scroll , 1985, IEEE Conference on Decision and Control.

[28]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[29]  Xiaofan Wang,et al.  On synchronization in scale-free dynamical networks , 2005 .

[30]  Lilian Huang,et al.  Synchronization of chaotic systems via nonlinear control , 2004 .

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

[32]  Seon Hee Park,et al.  MULTISTABILITY IN COUPLED OSCILLATOR SYSTEMS WITH TIME DELAY , 1997 .

[33]  Diego Pazó,et al.  Time delay in the Kuramoto model with bimodal frequency distribution. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  L Chen,et al.  Synchronization with on-off coupling: Role of time scales in network dynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.