Novel decentralized adaptive strategies for the synchronization of complex networks

This paper is concerned with the analysis of the synchronization of networks of nonlinear oscillators through an innovative local adaptive approach. In particular, time-varying feedback coupling gains are considered, whose gradient is a function of the local synchronization error over each edge in the network. It is shown that, under appropriate conditions, the strategy is indeed successful in guaranteeing the achievement of a common synchronous evolution for all oscillators in the network. The theoretical derivation is complemented by its validation on a set of representative examples.

[1]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[2]  Xiwei Chen,et al.  Network Synchronization with an Adaptive Coupling Strength , 2006 .

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

[4]  Changsong Zhou,et al.  Dynamical weights and enhanced synchronization in adaptive complex networks. , 2006, Physical review letters.

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

[6]  J. Fewell Social Insect Networks , 2003, Science.

[7]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[8]  F. Garofalo,et al.  Synchronization of complex networks through local adaptive coupling. , 2008, Chaos.

[9]  L. Chua,et al.  The double hook (nonlinear chaotic circuits) , 1988 .

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

[11]  J. Kurths,et al.  Synchronization in the Kuramoto model: a dynamical gradient network approach. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Licheng Jiao,et al.  Robust adaptive global synchronization of complex dynamical networks by adjusting time-varying coupling strength , 2008 .

[13]  M. Spong,et al.  On Synchronization of Kuramoto Oscillators , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[14]  Benjamin Van Roy,et al.  Distributed Optimization in Adaptive Networks , 2003, NIPS.

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

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

[17]  Takashi Matsumoto,et al.  A chaotic attractor from Chua's circuit , 1984 .

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

[19]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .

[20]  Zoltan Toroczkai,et al.  Gradient Networks , 2004, cond-mat/0408262.

[21]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

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

[23]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Risto Miikkulainen,et al.  Evolving adaptive neural networks with and without adaptive synapses , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

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