On the Approximation of Complicated Dynamical Behavior

Dellnitz, Michael; Junge, Oliver

doi:10.1007/978-0-387-21830-4_22

Cited by 194 publications

(380 citation statements)

References 21 publications

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“…As shown in the figure, the MM is fairly accurate in describing the asymptotic behavior of the system in terms of probabilities. also suggests oscillations in the asymptotic dynamics; cf., [39], [40], [47]. This is indeed consistent with the results of the time-domain simulation which exhibit oscillations in the nonequilibrium regime.…”

Section: Stochastic Model and Bifurcation Analysissupporting

confidence: 90%

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A non-equilibrium analysis and control framework for active queue management

et al. 2008

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Section: Stochastic Model and Bifurcation Analysissupporting

confidence: 90%

“…P is interpreted as an pproximation of P obtained by considering a certain random perturbation of the dynamical system T . P converges to P in L 2 as the partition gets finer and finer [39].…”

Section: Stochastic Model and Bifurcation Analysismentioning

confidence: 96%

A non-equilibrium analysis and control framework for active queue management

et al. 2008

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“…The transfer operator methods developed in Ref. 12 reveal the locations of the ocean garbage patches. We further adapt these methods to decompose the surface ocean into almost-invariant sets in a forward-time and backward-time sense.…”

Section: Introductionmentioning

confidence: 99%

How well-connected is the surface of the global ocean?

Froyland

Stuart

Sebille

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

117

153

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The Ekman dynamics of the ocean surface circulation is known to contain attracting regions such as the great oceanic gyres and the associated garbage patches. Less well-known are the extents of the basins of attractions of these regions and how strongly attracting they are. Understanding the shape and extent of the basins of attraction sheds light on the question of the strength of connectivity of different regions of the ocean, which helps in understanding the flow of buoyant material like plastic litter. Using short flow time trajectory data from a global ocean model, we create a Markov chain model of the surface ocean dynamics. The surface ocean is not a conservative dynamical system as water in the ocean follows three-dimensional pathways, with upwelling and downwelling in certain regions. Using our Markov chain model, we easily compute net surface upwelling and downwelling, and verify that it matches observed patterns of upwelling and downwelling in the real ocean. We analyze the Markov chain to determine multiple attracting regions. Finally, using an eigenvector approach, we (i) identify the five major ocean garbage patches, (ii) partition the ocean into basins of attraction for each of the garbage patches, and (iii) partition the ocean into regions that demonstrate transient dynamics modulo the attracting garbage patches. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4892530]Ocean dynamics operate and affect climate on timescales of months to millenia. In this paper, we investigate phenomena on the ocean's surface that manifest over very long time periods: we look for regions in which water, biomass, and pollutants become trapped "forever" (which we refer to as attracting regions), or for long periods of time before eventually exiting (which we refer to as almostinvariant regions). While attracting regions may be quite small in size or irregular in shape, they can nonetheless exert great influence on the global ocean surface dynamics if their basins of attraction are large.

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“…Invariant measures of the system can be identified with eigenfunctions of the Frobenius-Perron operator to the eigenvalue 1. In (Dellnitz and Junge 1999) the spectrum of the Frobenius-Perron operator is numerically approximated by analysing the spectrum of discrete approximations to the Frobenius-Perron operator. This is successfully applied to model the dynamics of complex bio molecules, see (Huisinga 2001) and (Schütte and Huisinga 2003).…”

Section: Macroscopic Models and Markov Chainsmentioning

confidence: 99%

Markov Chain Based Emissions Models: A Precursor for Green Control

Crisostomi

Kirkland

Schlote

et al. 2011

Green IT: Technologies and Applications

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In this chapter we propose a new method of modelling urban pollutants arising from transportation networks. The efficacy of the proposed approach is demonstrated by means of a number of examples. Our models give rise to a number of surprising observations that are relevant for the regulation of pollution in urban networks: Different actions are required for the control of different pollutants and low speed limits do not necessarily lead to low pollution.

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On the Approximation of Complicated Dynamical Behavior

Cited by 194 publications

References 21 publications

A non-equilibrium analysis and control framework for active queue management

A non-equilibrium analysis and control framework for active queue management

How well-connected is the surface of the global ocean?

Markov Chain Based Emissions Models: A Precursor for Green Control

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