12 research outputs found

    Synchronization and information transmission in networks

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    The amount of information produced by a network may be measured by the mutual information rate. This measure, the Kolmogorov-Sinai entropy and the synchronization interval are expressed in terms of the transversal Lyapunov exponents. Thus, these concepts are related and we proved that the larger the synchronization is, the larger the rate with which information is exchanged between nodes in the network. In fact, as the coupling parameter increases, the mutual information rate increases to a maximum at the synchronization interval and then decreases. Moreover, the Kolmogorov-Sinai entropy decreases until reaching a minimum at the synchronization interval and then increases. We present some numerical simulations considering two different versions of coupling two maps, a complete network and a lattice, which confirmed our theoretical results

    Chaotic synchronization of Piecewise Linear Maps

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    We derive a threshold value for the coupling strength in terms of the topological entropy, to achieve synchronization of two coupled piecewise linear maps, for the unidirectional and for the bidirectional coupling. We prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the bidirectional coupling of two identical chaotic Duffing equations is given

    Networks Synchronizability, Local Dynamics and Some Graph Invariants

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    The synchronization of a network depends on a number of factors, including the strength of the coupling, the connection topology and the dynamical behaviour of the individual units. In the first part of this work, we fix the network topology and obtain the synchronization interval in terms of the Lyapounov exponents for piecewise linear expanding maps in the nodes. If these piecewise linear maps have the same slope ¬Īs everywhere, we get a relation between synchronizability and the topological entropy. In the second part of this paper we fix the dynamics in the individual nodes and address our work to the study of the effect of clustering and conductance in the amplitude of the synchronization interval

    Spectral and Dynamical Invariants in a Complete Clustered Network

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    The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal

    Spectral and Dynamical Invariants in a Complete Clustered Network

    No full text
    The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal
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