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Networks from flows--from dynamics to topology.

Molkenthin N, Rehfeld K, Marwan N, Kurths J - Sci Rep (2014)

Bottom Line: Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure.Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks.The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.

View Article: PubMed Central - PubMed

Affiliation: 1] Potsdam Institute for Climate Impact Research, P.O.Box 601203, 14412 Potsdam, Germany [2] Department of Physics, Humboldt-Universit├Ąt zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.

ABSTRACT
Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.

No MeSH data available.


Flow field and network measures for the counter-currents in Fig. (1a).(a) The normed degree, relates to (b) the absolute value of the flow's local velocity; (c) The maxima of the normed betweenness are co-located with (d) the maxima of the absolute value of the gradient gradient of the absolute current velocity. See equations (14) and (15) for definitions of the network measures.
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f2: Flow field and network measures for the counter-currents in Fig. (1a).(a) The normed degree, relates to (b) the absolute value of the flow's local velocity; (c) The maxima of the normed betweenness are co-located with (d) the maxima of the absolute value of the gradient gradient of the absolute current velocity. See equations (14) and (15) for definitions of the network measures.

Mentions: We compute networks for the analytically homogeneous case (SM) and, using numerical integration, for two basic, low-gradient velocity fields given in Fig. 1, where i) one is composed of three narrow parallel flows, with alternating directions, and ii) the other flow is made up of two narrow flows intersecting in the middle. The resulting networks and underlying flows are illustrated in Fig. 1. Please note that the image resolution is equal to the grid resolution in all network figures. In areas of the flow with a higher velocity, the resulting networks show a higher density and length of links than in slower regions. We analyze these networks using the network measures degree ki (equation (14)) and betweenness centrality bi (equation (15)), in order to find relationships between them and the underlying velocity field. The network measures are given in Figs. 2 and 3.


Networks from flows--from dynamics to topology.

Molkenthin N, Rehfeld K, Marwan N, Kurths J - Sci Rep (2014)

Flow field and network measures for the counter-currents in Fig. (1a).(a) The normed degree, relates to (b) the absolute value of the flow's local velocity; (c) The maxima of the normed betweenness are co-located with (d) the maxima of the absolute value of the gradient gradient of the absolute current velocity. See equations (14) and (15) for definitions of the network measures.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3927207&req=5

f2: Flow field and network measures for the counter-currents in Fig. (1a).(a) The normed degree, relates to (b) the absolute value of the flow's local velocity; (c) The maxima of the normed betweenness are co-located with (d) the maxima of the absolute value of the gradient gradient of the absolute current velocity. See equations (14) and (15) for definitions of the network measures.
Mentions: We compute networks for the analytically homogeneous case (SM) and, using numerical integration, for two basic, low-gradient velocity fields given in Fig. 1, where i) one is composed of three narrow parallel flows, with alternating directions, and ii) the other flow is made up of two narrow flows intersecting in the middle. The resulting networks and underlying flows are illustrated in Fig. 1. Please note that the image resolution is equal to the grid resolution in all network figures. In areas of the flow with a higher velocity, the resulting networks show a higher density and length of links than in slower regions. We analyze these networks using the network measures degree ki (equation (14)) and betweenness centrality bi (equation (15)), in order to find relationships between them and the underlying velocity field. The network measures are given in Figs. 2 and 3.

Bottom Line: Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure.Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks.The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.

View Article: PubMed Central - PubMed

Affiliation: 1] Potsdam Institute for Climate Impact Research, P.O.Box 601203, 14412 Potsdam, Germany [2] Department of Physics, Humboldt-Universit├Ąt zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.

ABSTRACT
Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.

No MeSH data available.