Hybrid synchronization of the general delayed and non-delayed complex dynamical networks via pinning control

This paper investigates the hybrid synchronization problem of two coupled complex dynamical networks with non-delayed and delayed coupling by the pinning control strategy. Based on the LaSalle invariance principle and linear matrix inequality technique, we obtain some sufficient conditions for the hybrid synchronization by applying the simple linear feedback and adaptive controllers to a part of nodes. Under suitable conditions, two coupled networks can reach the hybrid synchronization, i.e., the outer synchronization between the drive and response networks, and the inner synchronization in each network simultaneously. Numerical simulations show the effectiveness of the proposed synchronization scheme.

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

[2]  Sha Wang,et al.  Hybrid projective synchronization of chaotic fractional order systems with different dimensions , 2010 .

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

[4]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[5]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[6]  Zhong Chen,et al.  An intriguing hybrid synchronization phenomenon of two coupled complex networks , 2010, Appl. Math. Comput..

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

[8]  Liang Chen,et al.  Adaptive synchronization between two complex networks with nonidentical topological structures , 2008 .

[9]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Jun Zhao,et al.  Synchronization of Complex Dynamical Networks with Switching Topology: a Switched System Point of View , 2008 .

[11]  Jinde Cao,et al.  Global synchronization in arrays of delayed neural networks with constant and delayed coupling , 2006 .

[12]  Her-Terng Yau,et al.  Synchronization and anti-synchronization coexist in two-degree-of-freedom dissipative gyroscope with nonlinear inputs , 2008 .

[13]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[14]  Zengrong Liu,et al.  Robust impulsive synchronization of complex delayed dynamical networks , 2008 .

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

[16]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

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

[18]  Yongguang Yu,et al.  Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design , 2011 .

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

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

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

[22]  Aihua Hu,et al.  Pinning a complex dynamical network via impulsive control , 2009 .

[23]  Juhn-Horng Chen,et al.  Synchronization and anti-synchronization coexist in Chen–Lee chaotic systems , 2009 .

[24]  Guanrong Chen,et al.  Hybrid chaos synchronization and its application in information processing , 2002 .

[25]  Jinde Cao,et al.  Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays , 2010 .

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

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

[28]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[29]  Tiedong Ma,et al.  On the exponential synchronization of stochastic impulsive chaotic delayed neural networks , 2011, Neurocomputing.

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

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

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

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

[34]  Jinde Cao,et al.  Adaptive synchronization of uncertain dynamical networks with delayed coupling , 2008 .

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

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

[37]  W. Zheng,et al.  Generalized outer synchronization between complex dynamical networks. , 2009, Chaos.