Generalized synchronization in complex networks

The phenomenon of generalized synchronization (GS) in networks with a complex topology of links between elements (nodes) representing chaotic dynamical systems has been studied. It is shown that GS onset in these networks can be detected as the moment of transition of the second-order Lyapunov exponent from a positive to a negative value. The results of the analysis are confirmed by the nearest-neighbor method. It is established that the network topology significantly influences the GS development.

[1]  Olga I. Moskalenko,et al.  Mechanisms behind the generalized synchronization conditions , 2006, nlin/0602054.

[2]  Yao-Chen Hung,et al.  Paths to globally generalized synchronization in scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Appearance of generalized synchronization in mutually coupled beam-plasma systems , 2011 .

[4]  Alexey A. Koronovskii,et al.  Synchronization in Networks of Slightly nonidentical Elements , 2008, Int. J. Bifurc. Chaos.

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

[6]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Nearest neighbors, phase tubes, and generalized synchronization. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Alexey A Koronovskii,et al.  Generalized synchronization: a modified system approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Kestutis Pyragas.  Conditional Lyapunov exponents from time series , 1997 .

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

[11]  S. A. Shurygina,et al.  The influence of the coupling mutuality degree on the onset of various types of chaotic synchronization , 2011 .

[12]  P. Woafo,et al.  Transitions from spatiotemporal chaos to cluster and complete synchronization states in a shift-invariant set of coupled nonlinear oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[15]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .