Chaos synchronization in networks of coupled maps with time-varying
topologies |
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Authors: | W L Lu F M Atay J Jost |
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Institution: | (1) Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany;(2) Lab. of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, 200433, Shanghai, P.R. China |
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Abstract: | Complexity of dynamical networks can arise not only from
the complexity of the topological structure but also from the time
evolution of the topology. In this paper, we study the synchronous
motion of coupled maps in time-varying complex networks both
analytically and numerically. The temporal variation is rather
general and formalized as being driven by a metric dynamical system.
Four network models are discussed in detail in which the
interconnections between vertices vary through time randomly. These
models are: 1) i.i.d. sequences of random graphs with fixed wiring
probability, 2) groups of graphs with random switches between the
individual graphs, 3) graphs with temporary random failures of
nodes, and 4) the meet-for-dinner model where the vertices are
randomly grouped. We show that the temporal variation and randomness
of the connection topology can enhance synchronizability in many
cases; however, there are also instances where they reduce
synchronizability. In analytical terms, the Hajnal diameter of the
coupling matrix sequence is presented as a measure for the
synchronizability of the graph topology. In topological terms, the
decisive criterion for synchronization of coupled chaotic maps is
that the union of the time-varying graphs contains a spanning tree. |
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Keywords: | PACS" target="_blank">PACS 05 45 Ra Coupled map lattices 05 45 Xt Synchronization coupled oscillators 02 50 Ey Stochastic processes |
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