Adaptive pinning control for the projective synchronization of drive-response dynamical networks

Abstract This paper studies the projective synchronization of a drive-response dynamical network of partially linear systems. The coupling-configuration matrix of the network is not necessarily symmetric. Two adaptive pinning control strategies are derived based on the Barbalat’s Lemma. In the first control strategy, the pinning control gain is adaptively updated to realize the projective synchronization. In the second control strategy, both the pinning control gain and the coupling strength between nodes are adaptively updated. Numerical simulation results show that the coupling strength needed in the second control strategy is smaller than that in the first control strategy to achieve the projective synchronization of the network.

[1]  Daolin Xu,et al.  Controlled Projective Synchronization in Nonpartially-Linear Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[2]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[3]  Guohui Li,et al.  Projective synchronization of chaotic system using backstepping control , 2006 .

[4]  Yi-Zheng Fan,et al.  Adaptive synchronization in complex dynamical networks with coupling delays for general graphs , 2012, Appl. Math. Comput..

[5]  Naoko Nakagawa,et al.  Collective Chaos in a Population of Globally Coupled Oscillators , 1993 .

[6]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[7]  Manfeng Hu,et al.  Adaptive feedback controller for projective synchronization , 2008 .

[8]  Ho-Youl Jung,et al.  Synchronization of a delayed complex dynamical network with free coupling matrix , 2012 .

[9]  M. Cross,et al.  Pinning control of spatiotemporal chaos , 1997, chao-dyn/9705001.

[10]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[11]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

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

[13]  D Xu,et al.  Control of projective synchronization in chaotic systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  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.

[15]  Lixin Tian,et al.  Projective synchronization in drive-response dynamical networks of partially linear systems with time-varying coupling delay , 2008 .

[16]  S. Bishop,et al.  Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems. , 2001, Chaos.

[17]  Song Zheng,et al.  Adaptive modified function projective synchronization of unknown chaotic systems with different order , 2012, Appl. Math. Comput..

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

[19]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[20]  Daolin Xu,et al.  Stability criterion for projective synchronization in three-dimensional chaotic systems , 2001 .

[21]  Ming Cao,et al.  Generalized synchronization in complex dynamical networks via adaptive couplings , 2010 .

[22]  Jianping Yan,et al.  Generalized projective synchronization of a unified chaotic system , 2005 .

[23]  Massimo Marchiori,et al.  How the science of complex networks can help developing strategies against terrorism , 2004 .

[24]  Jinhu Lu,et al.  Erratum to: "Pinning adaptive synchronization of a general complex dynamical network" [Automatica 44 (2008) 996-1003] , 2009, Autom..

[25]  Ju H. Park,et al.  Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling , 2012, Appl. Math. Comput..

[26]  Tao Wang,et al.  Chaos control and hybrid projective synchronization of several new chaotic systems , 2012, Appl. Math. Comput..

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

[28]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[29]  Tomoki Fukai,et al.  Gamma frequency synchronization in a local cortical network model , 2004, Neurocomputing.

[30]  Yinping Zhang,et al.  Chaotic synchronization and anti-synchronization based on suitable separation , 2004 .

[31]  Francesca Fiorilli,et al.  Experiments on node-to-node pinning control of Chua’s circuits , 2010 .

[32]  Daolin Xu,et al.  Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Maurizio Porfiri,et al.  Criteria for global pinning-controllability of complex networks , 2008, Autom..

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

[35]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[36]  Mario di Bernardo,et al.  Novel decentralized adaptive strategies for the synchronization of complex networks , 2009, Autom..

[37]  Junan Lu,et al.  Pinning adaptive synchronization of a general complex dynamical network , 2008, Autom..

[38]  Daolin Xu,et al.  Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems , 2005 .

[39]  Shihua Chen,et al.  Pinning synchronization of the complex networks with non-delayed and delayed coupling , 2009 .

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