Measuring critical transitions in financial markets

Jurczyk, Jan; Rehberg, Thorsten; Eckrot, Alexander; Morgenstern, Ingo

doi:10.1038/s41598-017-11854-1

Cited by 38 publications

(19 citation statements)

References 45 publications

(35 reference statements)

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“…Tipping point transitions refer to abrupt changes in the state of a dynamical system caused by a rapid transition from an equilibrium state of the system to another equilibrium. Such transitions have been observed in many systems such as climate dynamics 1,2 , epilepsy 3-5 , population ecology [6][7][8] , fluid dynamics 9,10 , and stock markets [11][12][13] . Typically, one of the system equilibria is desirable and transitions away from it are catastrophic.…”

Section: Introductionmentioning

confidence: 99%

Mitigation of tipping point transitions by time-delay feedback control

Farazmand

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria is possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the system stays near a desirable equilibrium. For small delays, we show that the control term has two effects: i) a stabilizing effect by deepening the potential well around the desirable equilibrium, and ii) a destabilizing effect by intensifying the noise by a factor of (1 − τ α) −1/2 , where τ and α denote the delay and the control gain, respectively. As a result, successful mitigation depends on the competition between these two factors. We also derive analytical results that elucidate the choice of the appropriate control gain and delay that ensure successful mitigations. These results eliminate the need for any Monte Carlo simulations of the stochastic differential equations, and therefore significantly reduce the computational cost of determining the suitable control parameters. We demonstrate the application of our results on two examples.Many complex systems, such as the climate, stock markets, population of species, and the nervous system, have multiple stable equilibrium states. Near the tipping point of the system, small amounts of stochastic disturbances can lead to transitions between these equilibria. Typically, one of the equilibria is desirable and transitions away from it lead to catastrophic consequences. Here, we analyze the ability of a delay feedback control to mitigate transitions away from a desirable equilibrium. arXiv:1911.05292v2 [math.OC]

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Section: Introductionmentioning

confidence: 99%

Mitigation of tipping point transitions by time-delay feedback control

Farazmand

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Random Matrix Theory is one of the useful methods for analyzing the behavior of complex systems [16,[43][44][45][46][47][48][49][50][51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Global Banking Network by Random Matrix Theory

et al. 2021

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Since the financial crisis of 2008, the network analysis of financial systems has attracted a lot of attention. In this paper, we analyze the global banking network via the method of Random Matrix Theory. By applying that method on a cross border lending network, it is shown that while the connectivity between different parts of the network has risen and the profile of transactions has diversified, the role of hubs remains important in the weighted perspective. The largest eigenvalue of the transaction matrix as the leading mode of the system shows sharp growth since 2002. As well, it is observed that its growth has diminished since 2008. This indicates that the crisis of 2008 has left a long-lasting footprint on the financial system. Analyzing the mean value of the participation ratio reveals the fact that the role of countries in forming small modes, has increased since 2002. In our final analysis, we provide snapshots of the hubs in the network over time. We observe that the share of countries in total transactions is not equal to their share in shaping the eigenvector of the largest eigenvalue. In 2018 for example, while the United Kingdom leads the share of transactions, it is the United States that has the largest value in the leading eigenvector. The proposed technique in the paper can be useful for analyzing different types of interaction networks between countries.

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“…In biology, energy landscapes are central to understanding the microscopic origins of processes, including protein folding (3)(4)(5)(6)(7)(8) and selective transport through membrane channels (9)(10)(11)(12)(13)(14). Elucidating the factors governing the dynamics of stochastic processes may be central to even more diverse problems, such as understanding electron transport (15) or the changing stock prices in financial markets (16)(17)(18). Despite this, quantitatively resolving the energy landscape that governs an arbitrary process is, in general, very difficult and requires measurements of transition path times (3,4,(19)(20)(21).…”

Section: Introductionmentioning

confidence: 99%

Direct detection of molecular intermediates from first-passage times

et al. 2020

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All natural phenomena are governed by energy landscapes. However, the direct measurement of this fundamental quantity remains challenging, particularly in complex systems involving intermediate states. Here, we uncover key details of the energy landscapes that underpin a range of experimental systems through quantitative analysis of first-passage time distributions. By combined study of colloidal dynamics in confinement, transport through a biological pore, and the folding kinetics of DNA hairpins, we demonstrate conclusively how a short-time, power-law regime of the first-passage time distribution reflects the number of intermediate states associated with each of these processes, despite their differing length scales, time scales, and interactions. We thereby establish a powerful method for investigating the underlying mechanisms of complex molecular processes.

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Measuring critical transitions in financial markets

Cited by 38 publications

References 45 publications

Mitigation of tipping point transitions by time-delay feedback control

Mitigation of tipping point transitions by time-delay feedback control

Analysis of the Global Banking Network by Random Matrix Theory

Direct detection of molecular intermediates from first-passage times

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