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Kuske, Rachel

doi:10.1023/a:1004658609270

Cited by 28 publications

(5 citation statements)

References 16 publications

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“…A way to estimate the hazard represented by the delayed bifurcation is to compute, using the surrogate model, the statistic of the time t fp needed to reach a certain danger level. This is similar to the classical problem of first passage time, often addressed in the context of bifurcation theory for stochastic dynamics in steady double-well potential [3,[55][56][57][58]. A major difference in the present situation is that the potential evolves with time.…”

Section: First Passage Analysismentioning

confidence: 74%

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

et al. 2018

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Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions.

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Section: First Passage Analysismentioning

confidence: 74%

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

et al. 2018

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“…This result follows Bartlett [34], who showed that very low sparking rates could generate long time lags between recurrent outbreaks. In dynamic bifurcations more generally, the addition of stochasticity or noise to slow passages through bifurcation points reduces bifurcation delay [35,36] by hastening the departure from an unstable equilibrium. While our results are in agreement, we also note that 'noise' in our system is strictly required for the critical transition to disease emergence.…”

Section: Discussionmentioning

confidence: 99%

Waiting time to infectious disease emergence

Dibble

O’Dea

Park

et al. 2016

J. R. Soc. Interface.

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Emerging diseases must make a transition from stuttering chains of transmission to sustained chains of transmission, but this critical transition need not coincide with the system becoming supercritical. That is, the introduction of infection to a supercritical system results in a significant fraction of the population becoming infected only with a certain probability. Understanding the waiting time to the first major outbreak of an emerging disease is then more complicated than determining when the system becomes supercritical. We treat emergence as a dynamic bifurcation, and use the concept of bifurcation delay to understand the time to emergence after a system becomes supercritical. Specifically, we consider an SIR model with a time-varying transmission term and random infections originating from outside the population. We derive an analytic density function for the delay times and find it to be, in general, in agreement with stochastic simulations. We find the key parameters to be the rate of introduction of infection and the rate of change of the basic reproductive ratio. These findings aid our understanding of real emergence events, and can be incorporated into early-warning systems aimed at forecasting disease risk.

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“…In some works, dynamical systems are treated in a probabilistic way and noise effects on bifurcations are studied [13][14][15][16]. A different approach has been used in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…The derivation of amplitude equations for randomly forced dynamical systems has been previously considered in the literature. In some works, dynamical systems are treated in a probabilistic way and noise effects on bifurcations are studied [13,14,15,16]. A different approach has been used in references [17,18] where the authors derive a stochastic Landau form as the amplitude equation for the stochastic Swift-Hohenberg model and use it to describe the dynamics of the bifurcating solutions.…”

Section: Introductionmentioning

confidence: 99%

Derivation of amplitude equations for nonlinear oscillators subject to arbitrary forcing

2004

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By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero-dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be straightforwardly applied to the case that the forcing is white noise. We give examples of the use of this method to the case of the van der Pol-Duffing oscillator. The writing of the amplitude equations in terms of a Lyapunov potential allow us to obtain an analytical expression for the probability distribution function which reproduces reasonably well the numerical simulation results.

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Untitled

Cited by 28 publications

References 16 publications

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Waiting time to infectious disease emergence

Derivation of amplitude equations for nonlinear oscillators subject to arbitrary forcing

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