scholarly journals Critical transitions in heterogeneous networks: Loss of low-degree nodes as an early warning signal

2019 ◽  
Vol 99 (4) ◽  
Author(s):  
Alessandro Loppini ◽  
Simonetta Filippi ◽  
H. Eugene Stanley
Author(s):  
Edmund Barter ◽  
Andreas Brechtel ◽  
Barbara Drossel ◽  
Thilo Gross

The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closed-form analytical solution for the calculation of a system’s Jacobian from a time series. Being able to access the Jacobian enables a broad range of mathematical analyses by which deeper insights into the system can be gained. Here we consider in particular the computation of the leading Jacobian eigenvalue as an early warning signal for critical transitions. To illustrate this approach, we apply it to ecological meta-foodweb models, which are strongly nonlinear dynamical multi-layer networks. Our analysis shows that accurate results can be obtained, although the data demand of the method is still high.


2019 ◽  
Vol 62 (5) ◽  
pp. 1307-1332 ◽  
Author(s):  
Daniel L. Gamache ◽  
Gerry McNamara ◽  
Scott D. Graffin ◽  
Jason Kiley ◽  
Jerayr Haleblian ◽  
...  

Chemoecology ◽  
2008 ◽  
Vol 18 (4) ◽  
pp. 255-261 ◽  
Author(s):  
Meaghan A. Vavrek ◽  
Chris K. Elvidge ◽  
Robert DeCaire ◽  
Brenna Belland ◽  
Christopher D. Jackson ◽  
...  

2008 ◽  
Vol 105 (38) ◽  
pp. 14308-14312 ◽  
Author(s):  
V. Dakos ◽  
M. Scheffer ◽  
E. H. van Nes ◽  
V. Brovkin ◽  
V. Petoukhov ◽  
...  

2015 ◽  
Vol 370 (1659) ◽  
pp. 20130263 ◽  
Author(s):  
Vasilis Dakos ◽  
Stephen R. Carpenter ◽  
Egbert H. van Nes ◽  
Marten Scheffer

In the vicinity of tipping points—or more precisely bifurcation points—ecosystems recover slowly from small perturbations. Such slowness may be interpreted as a sign of low resilience in the sense that the ecosystem could easily be tipped through a critical transition into a contrasting state. Indicators of this phenomenon of ‘critical slowing down (CSD)’ include a rise in temporal correlation and variance. Such indicators of CSD can provide an early warning signal of a nearby tipping point. Or, they may offer a possibility to rank reefs, lakes or other ecosystems according to their resilience. The fact that CSD may happen across a wide range of complex ecosystems close to tipping points implies a powerful generality. However, indicators of CSD are not manifested in all cases where regime shifts occur. This is because not all regime shifts are associated with tipping points. Here, we review the exploding literature about this issue to provide guidance on what to expect and what not to expect when it comes to the CSD-based early warning signals for critical transitions.


2013 ◽  
Vol 6 (3) ◽  
pp. 309-317 ◽  
Author(s):  
Vasilis Dakos ◽  
Egbert H. van Nes ◽  
Marten Scheffer

2020 ◽  
Author(s):  
Lidia Ceriani ◽  
Carlos Hernandez-Suarez ◽  
Paolo Verme

AbstractThe paper provides some initial evidence that daily mortality rates (for any cause) by municipality or province can be used as a statistically reliable predictor of looming COVID-19 crises. Using recently published deaths figures for 1,689 Italian municipalities, we estimate the growth in daily mortality rates between the period 2015–2019 and 2020 by province. All provinces that experienced a major COVID-19 shock in mid-March 2020 had increases in mortality rates of 100% or above already in early February 2020. This increase was particularly strong for males and older people, two recognizable features of COVID-19. Using a panel fixed effect model, we show that the association between these early increases in mortality for any cause and the March 2020 COVID-19 shock is strong and significant. We conclude that the growth in mortality rates can be used as a statistically reliable predictor of COVID-19 crises.


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