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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.


Related in: MedlinePlus

Schematic illustration of flow properties, that result in distinctive network properties: While advection dominates the transport of temperatire fluctuations in regions of fast propagation, localized diffusion dominates in stagnant regions.Signals that leave the stagnant area by diffusion through the mixed region are subsequently transmitted along the flow. This leads to the asymmetry seen in the betweenness, where the betweenness values rise in flow direction.
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f5: Schematic illustration of flow properties, that result in distinctive network properties: While advection dominates the transport of temperatire fluctuations in regions of fast propagation, localized diffusion dominates in stagnant regions.Signals that leave the stagnant area by diffusion through the mixed region are subsequently transmitted along the flow. This leads to the asymmetry seen in the betweenness, where the betweenness values rise in flow direction.

Mentions: We find that both, the degree and the betweenness increase marginally along the flow direction. This can be understood as the signals from the slow flowing region first travel through diffusion, once they hit the fast region their main peak will travel downstream (the trajectory approximately follows the red arrow in Fig. 5). This leads to points downstream in the fast flowing area to have connections even to points in the slow region upstream from them, leading to increased degree and betweenness there.


Networks from flows--from dynamics to topology.

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

Schematic illustration of flow properties, that result in distinctive network properties: While advection dominates the transport of temperatire fluctuations in regions of fast propagation, localized diffusion dominates in stagnant regions.Signals that leave the stagnant area by diffusion through the mixed region are subsequently transmitted along the flow. This leads to the asymmetry seen in the betweenness, where the betweenness values rise in flow direction.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Schematic illustration of flow properties, that result in distinctive network properties: While advection dominates the transport of temperatire fluctuations in regions of fast propagation, localized diffusion dominates in stagnant regions.Signals that leave the stagnant area by diffusion through the mixed region are subsequently transmitted along the flow. This leads to the asymmetry seen in the betweenness, where the betweenness values rise in flow direction.
Mentions: We find that both, the degree and the betweenness increase marginally along the flow direction. This can be understood as the signals from the slow flowing region first travel through diffusion, once they hit the fast region their main peak will travel downstream (the trajectory approximately follows the red arrow in Fig. 5). This leads to points downstream in the fast flowing area to have connections even to points in the slow region upstream from them, leading to increased degree and betweenness there.

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.


Related in: MedlinePlus