scholarly journals Deep learning for early warning signals of tipping points

2021 ◽  
Vol 118 (39) ◽  
pp. e2106140118 ◽  
Author(s):  
Thomas M. Bury ◽  
R. I. Sujith ◽  
Induja Pavithran ◽  
Marten Scheffer ◽  
Timothy M. Lenton ◽  
...  
Keyword(s):  
Deep Learning ◽  
Early Warning ◽  
Normal Forms ◽  
Learning Algorithm ◽  
Tipping Point ◽  
State Transitions ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Deep Learning Algorithm

Many natural systems exhibit tipping points where slowly changing environmental conditions spark a sudden shift to a new and sometimes very different state. As the tipping point is approached, the dynamics of complex and varied systems simplify down to a limited number of possible “normal forms” that determine qualitative aspects of the new state that lies beyond the tipping point, such as whether it will oscillate or be stable. In several of those forms, indicators like increasing lag-1 autocorrelation and variance provide generic early warning signals (EWS) of the tipping point by detecting how dynamics slow down near the transition. But they do not predict the nature of the new state. Here we develop a deep learning algorithm that provides EWS in systems it was not explicitly trained on, by exploiting information about normal forms and scaling behavior of dynamics near tipping points that are common to many dynamical systems. The algorithm provides EWS in 268 empirical and model time series from ecology, thermoacoustics, climatology, and epidemiology with much greater sensitivity and specificity than generic EWS. It can also predict the normal form that characterizes the oncoming tipping point, thus providing qualitative information on certain aspects of the new state. Such approaches can help humans better prepare for, or avoid, undesirable state transitions. The algorithm also illustrates how a universe of possible models can be mined to recognize naturally occurring tipping points.

scholarly journals Deep learning for early warning signals of regime shifts

2021 ◽  
Author(s):  
Thomas Bury ◽  
Raman Sujith ◽  
Induja Pavithran ◽  
Marten Scheffer ◽  
Timothy Lenton ◽  
...  
Keyword(s):  
Deep Learning ◽  
Early Warning ◽  
Normal Forms ◽  
Learning Algorithm ◽  
Tipping Point ◽  
Regime Shifts ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Deep Learning Algorithm

Many natural systems exhibit regime shifts where slowly changing environmental conditions suddenly shift the system to a new and sometimes very different state. As the tipping point is approached, the dynamics of complex and varied systems all simplify down to a small number of possible 'normal forms' that determine how the new regime will look. Indicators such as increasing lag-1 autocorrelation and variance provide generic early warning signals (EWS) by detecting how dynamics slow down near the tipping point. But they do not indicate what type of new regime will emerge. Here we develop a deep learning algorithm that can detect EWS in systems it was not explicitly trained on, by exploiting information about normal forms and scaling behaviour of dynamics near tipping points that are common to many dynamical systems. The algorithm detects EWS in 268 empirical and model time series from ecology, thermoacoustics, climatology, and epidemiology with much greater sensitivity and specificity than generic EWS. It can also predict the normal form that will characterize the oncoming regime shift. Such approaches can help humans better manage regime shifts. The algorithm also illustrates how a universe of possible models can be mined to recognize naturally-occurring tipping points.

scholarly journals Early warning signals of tipping points in periodically forced systems

2016 ◽  
Vol 7 (2) ◽  
pp. 313-326 ◽  
Author(s):  
Mark S. Williamson ◽  
Sebastian Bathiany ◽  
Timothy M. Lenton
Keyword(s):  
Sea Ice ◽  
Early Warning ◽  
Tipping Point ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
System Response ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Arctic Sea

Abstract. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.

scholarly journals Early warning signals of tipping points in periodically forced systems

2015 ◽  
Vol 6 (2) ◽  
pp. 2243-2272 ◽  
Author(s):  
M. S. Williamson ◽  
S. Bathiany ◽  
T. M. Lenton
Keyword(s):  
Sea Ice ◽  
Early Warning ◽  
Tipping Point ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
System Response ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Arctic Sea

Abstract. The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much recent interest. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we find alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose time scale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. We show that the phase lag and amplification of the system response provide early warning signals, based on a linear dynamics approximation. Furthermore, the power spectrum of the system's time series reveals the generation of harmonics of the forcing period, the size of which are proportional to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.

Alternative stable states, tipping points, and early warning signals of ecological transitions

2020 ◽  
pp. 263-284
Author(s):  
John M. Drake ◽  
Suzanne M. O’Regan ◽  
Vasilis Dakos ◽  
Sonia Kéfi ◽  
Pejman Rohani
Keyword(s):  
Early Warning ◽  
Alternative Stable States ◽  
Intrinsic Noise ◽  
Point Theory ◽  
Ecological Systems ◽  
Tipping Point ◽  
Stable States ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Theoretical Predictions

Ecological systems are prone to dramatic shifts between alternative stable states. In reality, these shifts are often caused by slow forces external to the system that eventually push it over a tipping point. Theory predicts that when ecological systems are brought close to a tipping point, the dynamical feedback intrinsic to the system interact with intrinsic noise and extrinsic perturbations in characteristic ways. The resulting phenomena thus serve as “early warning signals” for shifts such as population collapse. In this chapter, we review the basic (qualitative) theory of such systems. We then illustrate the main ideas with a series of models that both represent fundamental ecological ideas (e.g. density-dependence) and are amenable to mathematical analysis. These analyses provide theoretical predictions about the nature of measurable fluctuations in the vicinity of a tipping point. We conclude with a review of empirical evidence from laboratory microcosms, field manipulations, and observational studies.

scholarly journals Detecting and distinguishing tipping points using spectral early warning signals

2020 ◽  
Vol 17 (170) ◽  
pp. 20200482
Author(s):  
T. M. Bury ◽  
C. T. Bauch ◽  
M. Anand
Keyword(s):  
Complex Systems ◽  
Early Warning ◽  
Dynamical Regime ◽  
Tipping Points ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Density Dependent ◽  
Critical Transitions ◽  
Fold Bifurcation ◽  
Characteristic Signal

Theory and observation tell us that many complex systems exhibit tipping points—thresholds involving an abrupt and irreversible transition to a contrasting dynamical regime. Such events are commonly referred to as critical transitions. Current research seeks to develop early warning signals (EWS) of critical transitions that could help prevent undesirable events such as ecosystem collapse. However, conventional EWS do not indicate the type of transition, since they are based on the generic phenomena of critical slowing down. For instance, they may fail to distinguish the onset of oscillations (e.g. Hopf bifurcation) from a transition to a distant attractor (e.g. Fold bifurcation). Moreover, conventional EWS are less reliable in systems with density-dependent noise. Other EWS based on the power spectrum (spectral EWS) have been proposed, but they rely upon spectral reddening, which does not occur prior to critical transitions with an oscillatory component. Here, we use Ornstein–Uhlenbeck theory to derive analytic approximations for EWS prior to each type of local bifurcation, thereby creating new spectral EWS that provide greater sensitivity to transition proximity; higher robustness to density-dependent noise and bifurcation type; and clues to the type of approaching transition. We demonstrate the advantage of applying these spectral EWS in concert with conventional EWS using a population model, and show that they provide a characteristic signal prior to two different Hopf bifurcations in data from a predator–prey chemostat experiment. The ability to better infer and differentiate the nature of upcoming transitions in complex systems will help humanity manage critical transitions in the Anthropocene Era.

scholarly journals Dynamical state transitions into addictive behaviour and their early-warning signals

2017 ◽  
Vol 284 (1860) ◽  
pp. 20170882 ◽  
Author(s):  
Jerome Clifford Foo ◽  
Hamid Reza Noori ◽  
Ikuhiro Yamaguchi ◽  
Valentina Vengeliene ◽  
Alejandro Cosa-Linan ◽  
...  
Keyword(s):  
Early Warning ◽  
Alcohol Exposure ◽  
State Transitions ◽  
Drinking Behaviour ◽  
Disease Dynamics ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Addictive Behaviour ◽  
Excessive Alcohol ◽  
Biomedical Field

The theory of critical transitions in complex systems (ecosystems, climate, etc.), and especially its ability to predict abrupt changes by early-warning signals based on analysis of fluctuations close to tipping points, is seen as a promising avenue to study disease dynamics. However, the biomedical field still lacks a clear demonstration of this concept. Here, we used a well-established animal model in which initial alcohol exposure followed by deprivation and subsequent reintroduction of alcohol induces excessive alcohol drinking as an example of disease onset. Intensive longitudinal data (ILD) of rat drinking behaviour and locomotor activity were acquired by a fully automated drinkometer device over 14 weeks. Dynamical characteristics of ILD were extracted using a multi-scale computational approach. Our analysis shows a transition into addictive behaviour preceded by early-warning signals such as instability of drinking patterns and locomotor circadian rhythms, and a resultant increase in low frequency, ultradian rhythms during the first week of deprivation. We find evidence that during prolonged deprivation, a critical transition takes place pushing the system to excessive alcohol consumption. This study provides an adaptable framework for processing ILD from clinical studies and for examining disease dynamics and early-warning signals in the biomedical field.

scholarly journals Early-Warning Signals for the Onsets of Greenland Interstadials and the Younger Dryas–Preboreal Transition

2016 ◽  
Vol 29 (11) ◽  
pp. 4047-4056 ◽  
Author(s):  
Martin Rypdal
Keyword(s):  
Time Scales ◽  
Early Warning ◽  
High Frequency ◽  
Characteristic Time ◽  
Younger Dryas ◽  
Tipping Point ◽  
Warning Signals ◽  
Correlation Times ◽  
Early Warning Signals ◽  
Slowing Down

Abstract The climate system approaches a tipping point if the prevailing climate state loses stability, making a transition to a different state possible. A result from the theory of randomly driven dynamical systems is that the reduced stability in the vicinity of a tipping point is accompanied by increasing fluctuation levels and longer correlation times (critical slowing down) and can in principle serve as early-warning signals of an upcoming tipping point. This study demonstrates that the high-frequency band of the δ18O variations in the North Greenland Ice Core Project displays fluctuation levels that increase as one approaches the onset of an interstadial (warm) period. Similar results are found for the locally estimated Hurst exponent for the high-frequency fluctuations, signaling longer correlation times. The observed slowing down is found to be even stronger in the Younger Dryas, suggesting that both the Younger Dryas–Preboreal transition and the onsets of the Greenland interstadials are preceded by decreasing stability of the climate state. It is also verified that the temperature fluctuations during the stadial periods can be approximately modeled as a scale-invariant persistent noise, which can be approximated as an aggregation of processes that respond to perturbations on certain characteristic time scales. The results are consistent with the hypothesis that both the onsets of the Greenland interstadials and the Younger Dryas–Preboreal transition are caused by tipping points in dynamical processes with characteristic time scales on the order of decades and that the variability of other processes on longer time scales masks the early-warning signatures in the δ18O signal.

Sign in / Sign up

Export Citation Format

Share Document