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. 2011 Aug 11;6(8):e23378. doi: 10.1371/journal.pone.0023378

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Campanharo et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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Inline graphic — We use 10,000 time points of the variable of the chaotic Lorenz and Rossler equations and construct networks using quantiles by applying the forward map. Each node is colored according to the module to which it belongs. The resulting networks display clear differences in topologies. The network of Lorenz's system is bulky with two large modules. It has a modularity value of , that is much larger than the mean (standard error) modularity value obtained from networks built from the randomizations of the original time series. Furthermore, the two lobes of the Lorenz attractor are mapped into the two largest connected modules in the network. On the other hand, the network of Rossler's system presents an elongated, chain-like pattern due the strong periodicity present in its corresponding time series. The network of Rossler's system is also modular, with five small modules and it has a modularity value of . This value is much larger than the mean (standard error) modularity value obtained from networks built from the randomizations of the original time series.

We use 10,000 time points of the variable of the chaotic Lorenz and Rossler equations and construct networks using quantiles by applying the forward map. Each node is colored according to the module to which it belongs. The resulting networks display clear differences in topologies. The network of Lorenz's system is bulky with two large modules. It has a modularity value of , that is much larger than the mean (standard error) modularity value obtained from networks built from the randomizations of the original time series. Furthermore, the two lobes of the Lorenz attractor are mapped into the two largest connected modules in the network. On the other hand, the network of Rossler's system presents an elongated, chain-like pattern due the strong periodicity present in its corresponding time series. The network of Rossler's system is also modular, with five small modules and it has a modularity value of . This value is much larger than the mean (standard error) modularity value obtained from networks built from the randomizations of the original time series.