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Reverse engineering of complex dynamical networks in the presence of time-delayed interactions based on noisy time series
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10.1063/1.4747708
/content/aip/journal/chaos/22/3/10.1063/1.4747708
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/3/10.1063/1.4747708
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Figures

Image of FIG. 1.
FIG. 1.

Diagonal elements of the dynamical correlation matrix as a function of node degree k for three dynamical processes with different values of the time delay on scale-free and random networks. Square, circle, triangle and reverse triangle denote , 0.05, 0.07, and 0.09, respectively. The curves are the theoretical prediction from Eq. (15). The sizes of model networks are 100 and the average degree is 10. The noise strength is 0.1 and the coupling strength c is 0.2.

Image of FIG. 2.
FIG. 2.

Example of the distribution of the values of elements of the generalized inverse of the dynamical correlation matrix C for consensus dynamics associated with a scale-free network, where . The bimodal behavior is present for Kuramoto model and Rössler dynamics as well.

Image of FIG. 3.
FIG. 3.

Success rate of prediction of existent links for (a) consensus dynamics, (b) Kuramoto oscillators, and (c) Rössler dynamics as a function of time delay for a number of model and real-world networks: scale-free networks (scale-free),27 random network (random),28 small-world network (small-world),29 dolphin social network (dolphins),30 network of American football games among colleges (football),31 friendship network of karate club (karate),32 and network of political book purchases (book).33 Other parameters are the same as in Fig. 1. The success rate of nonexistent links is higher than 0.99 for all considered cases and thus are not shown.

Image of FIG. 4.
FIG. 4.

Predicted time delay from Eq. (19) versus the true (pre-assumed) values for the three dynamical processes on a number of model and real-world networks. The symbols denote the same networks as in Fig. 3. The lines are . Other parameters are the same as in Fig. 1.

Image of FIG. 5.
FIG. 5.

(a) Success rate of prediction of existent links as a function of the average time delay for different ranges of time delays for random consensus networks. (b) Predicted average time delay versus the original time delay for different ranges of time delay. The lines are . Other parameters are the same as in Fig. 1.

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/content/aip/journal/chaos/22/3/10.1063/1.4747708
2012-08-24
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Reverse engineering of complex dynamical networks in the presence of time-delayed interactions based on noisy time series
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/3/10.1063/1.4747708
10.1063/1.4747708
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