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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.


Flows and network measures for the crossing currents, see captio of Fig. 2.
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f3: Flows and network measures for the crossing currents, see captio of Fig. 2.

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)

Flows and network measures for the crossing currents, see captio of Fig. 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Flows and network measures for the crossing currents, see captio of Fig. 2.
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.