scholarly journals Critical slowing down in a dynamic duopoly

2015 ◽  
Vol 36 ◽  
pp. 1560012
Author(s):  
M. G. O. Escobido ◽  
N. Hatano
Keyword(s):  
Complex Systems ◽  
Dynamic Model ◽  
Early Warning ◽  
Critical Slowing Down ◽  
Economic Systems ◽  
Volterra System ◽  
Quantity Competition ◽  
Slowing Down ◽  
Critical Transitions ◽  
Dynamic Duopoly

Anticipating critical transitions is very important in economic systems as it can mean survival or demise of firms under stressful competition. As such identifying indicators that can provide early warning to these transitions are very crucial. In other complex systems, critical slowing down has been shown to anticipate critical transitions. In this paper, we investigate the applicability of the concept in the heterogeneous quantity competition between two firms. We develop a dynamic model where the duopoly can adjust their production in a logistic process. We show that the resulting dynamics is formally equivalent to a competitive Lotka-Volterra system. We investigate the behavior of the dominant eigenvalues and identify conditions that critical slowing down can provide early warning to the critical transitions in the dynamic duopoly.

scholarly journals Anticipating critical transitions in epithelial-hybrid-mesenchymal cell-fate determination

2019 ◽  
Author(s):  
Sukanta Sarkar ◽  
Sudipta Kumar Sinha ◽  
Herbert Levine ◽  
Mohit Kumar Jolly ◽  
Partha Sharathi Dutta
Keyword(s):  
Drug Resistance ◽  
Cell Fate ◽  
Early Warning ◽  
Cancer Metastasis ◽  
Critical Slowing Down ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Slowing Down ◽  
Tumor Relapse ◽  
Critical Transitions

AbstractIn the vicinity of a tipping point, critical transitions occur when small changes in an input condition causes sudden, large and often irreversible changes in the state of a system. Many natural systems ranging from ecosystems to molecular biosystems are known to exhibit critical transitions in their response to stochastic perturbations. In diseases, an early prediction of upcoming critical transitions from a healthy to a disease state by using early warning signals is of prime interest due to potential application in forecasting disease onset. Here, we analyze cell-fate transitions between different phenotypes (epithelial, hybrid epithelial/mesenchymal (E/M) and mesenchymal states) that are implicated in cancer metastasis and chemoresistance. These transitions are mediated by a mutually inhibitory feedback loop microRNA-200/ZEB driven by the levels of transcription factor SNAIL. We find that the proximity to tipping points enabling these transitions among different phenotypes can be captured by critical slowing down based early warning signals, calculated from the trajectory of ZEB mRNA level. Further, the basin stability analysis reveals the unexpectedly large basin of attraction for a hybrid E/M phenotype. Finally, we identified mechanisms that can potentially elude the transition to a hybrid E/M phenotype. Overall, our results unravel the early warning signals that can be used to anticipate upcoming epithelial-hybrid-mesenchymal transitions. With the emerging evidence about the hybrid E/M phenotype being a key driver of metastasis, drug resistance, and tumor relapse; our results suggest ways to potentially evade these transitions, reducing the fitness of cancer cells and restricting tumor aggressiveness.Significance StatementEpithelial-hybrid-mesenchymal transitions play critical roles in cancer metastasis, drug resistance, and tumor relapse. Recent studies have proposed that cells in a hybrid epithelial/mesenchymal phenotype may be more aggressive than those on either end of the spectrum. However, no biomarker to predict upcoming transitions has been identified. Here, we show that critical slowing down based early warning signals can detect sudden transitions among epithelial, hybrid E/M, and mesenchymal phenotypes. Importantly, our results highlight how stable a hybrid E/M phenotype can be, and how can a transition to this state be avoided. Thus, our study provides valuable insights into restricting cellular plasticity en route metastasis.

scholarly journals Anticipating Critical Transitions in Psychological Systems using Early Warning Signals: Theoretical and Practical Considerations

2020 ◽  
Author(s):  
Fabian Dablander ◽  
Anton Pichler ◽  
Arta Cika ◽  
Andrea Bacilieri
Keyword(s):  
Early Warning ◽  
Stable State ◽  
Critical Slowing Down ◽  
Future Research ◽  
Frequency Noise ◽  
Alternative Stable State ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Slowing Down ◽  
Critical Transitions

Many real-world systems can exhibit sudden shifts from one stable state to another, and the theory of dynamical systems points to the existence of generic early warning signals that precede such shifts. Recently, psychologists have begun to conceptualize mental disorders such as depression as an alternative stable state, and suggested that early warning signals based on the phenomenon of critical slowing down might be useful for predicting sudden transitions into depression or other psychiatric disorders. Harnessing the potential of early warning signals requires us to understand their limitations as well as the factors influencing their performance in practice. In this paper, we (a) review limitations of early warning signals based on critical slowing down to better understand when they can and cannot occur, and (b) study the conditions under which early warning signals may anticipate critical transitions in online-monitoring settings by simulating from a bistable dynamical system, varying crucial features such as sampling frequency, noise intensity, and speed of approaching the tipping point. We find that, in sharp contrast to their reputation of being generic or model-agnostic, whether early warning signals occur or not strongly depends on the specifics of the system. We also find that they are very sensitive to noise, potentially limiting their utility in practical applications. We discuss the implications of our findings and provide suggestions and recommendations for future research.

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 Early warning signals of malaria resurgence in Kericho, Kenya

2020 ◽  
Vol 16 (3) ◽  
pp. 20190713 ◽  
Author(s):  
Mallory J. Harris ◽  
Simon I. Hay ◽  
John M. Drake
Keyword(s):  
Early Warning ◽  
Disease Transmission ◽  
Empirical Test ◽  
Disease Incidence ◽  
Critical Slowing Down ◽  
Summary Statistics ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Slowing Down ◽  
Imported Case

Campaigns to eliminate infectious diseases could be greatly aided by methods for providing early warning signals of resurgence. Theory predicts that as a disease transmission system undergoes a transition from stability at the disease-free equilibrium to sustained transmission, it will exhibit characteristic behaviours known as critical slowing down, referring to the speed at which fluctuations in the number of cases are dampened, for instance the extinction of a local transmission chain after infection from an imported case. These phenomena include increases in several summary statistics, including lag-1 autocorrelation, variance and the first difference of variance. Here, we report the first empirical test of this prediction during the resurgence of malaria in Kericho, Kenya. For 10 summary statistics, we measured the approach to criticality in a rolling window to quantify the size of effect and directions. Nine of the statistics increased as predicted and variance, the first difference of variance, autocovariance, lag-1 autocorrelation and decay time returned early warning signals of critical slowing down based on permutation tests. These results show that time series of disease incidence collected through ordinary surveillance activities may exhibit characteristic signatures prior to an outbreak, a phenomenon that may be quite general among infectious disease systems.

scholarly journals Resilience indicators: prospects and limitations for early warnings of regime shifts

2015 ◽  
Vol 370 (1659) ◽  
pp. 20130263 ◽  
Author(s):  
Vasilis Dakos ◽  
Stephen R. Carpenter ◽  
Egbert H. van Nes ◽  
Marten Scheffer
Keyword(s):  
Early Warning ◽  
Temporal Correlation ◽  
Warning Signal ◽  
Regime Shifts ◽  
Tipping Points ◽  
Small Perturbations ◽  
Slowing Down ◽  
Critical Transitions ◽  
Wide Range ◽  
Resilience Indicators

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.

scholarly journals Transient indicators of tipping points in infectious diseases

2020 ◽  
Vol 17 (170) ◽  
pp. 20200094
Author(s):  
Suzanne M. O’Regan ◽  
Eamon B. O’Dea ◽  
Pejman Rohani ◽  
John M. Drake
Keyword(s):  
Infectious Diseases ◽  
Vaccine Uptake ◽  
Critical Slowing Down ◽  
Critical Threshold ◽  
Continuous Systems ◽  
Dominant Eigenvalue ◽  
Tipping Points ◽  
Critical Transition ◽  
Slowing Down ◽  
Critical Transitions

The majority of known early warning indicators of critical transitions rely on asymptotic resilience and critical slowing down. In continuous systems, critical slowing down is mathematically described by a decrease in magnitude of the dominant eigenvalue of the Jacobian matrix on the approach to a critical transition. Here, we show that measures of transient dynamics, specifically, reactivity and the maximum of the amplification envelope, also change systematically as a bifurcation is approached in an important class of models for epidemics of infectious diseases. Furthermore, we introduce indicators designed to detect trends in these measures and find that they reliably classify time series of case notifications simulated from stochastic models according to levels of vaccine uptake. Greater attention should be focused on the potential for systems to exhibit transient amplification of perturbations as a critical threshold is approached, and should be considered when searching for generic leading indicators of tipping points. Awareness of this phenomenon will enrich understanding of the dynamics of complex systems on the verge of a critical transition.

Re-thinking noise-induced tipping

2021 ◽  
Author(s):  
Julian Newman ◽  
Peter Ashwin
Keyword(s):  
Early Warning ◽  
Gaussian White Noise ◽  
External Noise ◽  
Critical Slowing Down ◽  
Critical Threshold ◽  
Geophysical Fluid Dynamics ◽  
Internal Dynamics ◽  
Slowing Down ◽  
The Earth ◽  
Joint Dynamics

<p>When modelling potential tipping elements of the earth system, one conventionally distinguishes "bifurcation-induced" and "noise-induced" tipping. The former occurs when an internal system parameter slowly crosses a critical threshold and external noise is negligible. The latter arises from forcing by noise well before a critical threshold for the internal dynamics is reached. The former comes with early warning signals, due to "critical slowing down" in the internal dynamics; but the latter occurs randomly without warning. However, these descriptions typically assume that the noise is Gaussian white noise, which arises as a limit of fast-timescale chaotic driving. We will instead consider, through a simple discrete-time prototype, finite-timescale bounded chaotic driving; this is a more suitable description of the subgrid forcing of turbulent geophysical fluid dynamics than uncorrelated noise. We will see that the phenomenon previously known as "noise-induced tipping" now corresponds to a deterministic bifurcation-induced tipping of the joint dynamics of the tipping element and the driving. Although "critical slowing down" does not occur in this bifurcation, early warning and near-exact prediction of the tipping event may still be possible. We also discuss the phenomenon of "noise-induced" prevention or delay of a tipping event, which cannot occur under conventional memoryless noise.</p>

scholarly journals Overlapping Time Scales Obscure Early Warning Signals for the Second COVID-19 Wave

2021 ◽  
Author(s):  
Fabian Dablander ◽  
Hans Heesterbeek ◽  
Denny Borsboom ◽  
John M. Drake
Keyword(s):  
Time Scales ◽  
Early Warning ◽  
Critical Slowing Down ◽  
Multiple Time Scales ◽  
Unexpected Finding ◽  
Multiple Time ◽  
Slowing Down ◽  
Early Warning Indicators ◽  
Second Wave ◽  
Warning Indicators

Early warning indicators based on critical slowing down have been suggested as a model-independent and low-cost tool to anticipate the (re)emergence of infectious diseases. We studied whether such indicators could reliably have anticipated the second COVID-19 wave in European countries. Contrary to theoretical predictions, we found that characteristic early warning indicators generally decreased rather than increased prior to the second wave. A model explains this unexpected finding as a result of transient dynamics and the multiple time scales of relaxation during a non-stationary epidemic. Particularly, if an epidemic that seems initially contained after a first wave does not fully settle to its new quasi-equilibrium prior to changing circumstances or conditions that force a second wave, then indicators will show a decreasing rather than an increasing trend as a result of the persistent transient trajectory of the first wave. Our simulations show that this lack of time scale separation was to be expected during the second European epidemic wave of COVID-19. Overall, our results emphasize that the theory of critical slowing down applies only when the external forcing of the system across a critical point is slow relative to the internal system dynamics.

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