Forecasting a class of bifurcations: Theory and experiment

Lim, Joosup; Epureanu, Bogdan I.

doi:10.1103/physreve.83.016203

Cited by 59 publications

(45 citation statements)

References 34 publications

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“…Reference [20] provides details regarding the use of λ to forecast bifurcations. In particular, Ref.…”

Section: Forecasting Bifurcationsmentioning

confidence: 99%

“…These techniques for forecasting bifurcations have been discussed for a diversity of applications, including ecosystems [5,7,22], climate systems [8], cell signaling [1], and ocean dynamics [15]. It has been demonstrated recently [20] that forecasting approaches can predict not only the bifurcation point, but also the type of bifurcation by monitoring the rates at which the system recovers from large perturbation levels. These techniques can also be applied to the engineered systems which generally require higher accuracy [20].…”

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confidence: 99%

“…It has been demonstrated recently [20] that forecasting approaches can predict not only the bifurcation point, but also the type of bifurcation by monitoring the rates at which the system recovers from large perturbation levels. These techniques can also be applied to the engineered systems which generally require higher accuracy [20]. The sensor output is sent to a real-time processor.…”

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confidence: 99%

“…To characterize bifurcations quickly and maintain the system in the safe pre-bifurcation regime during operation, the recent approach of forecasting bifurcations (developed by the authors [20]) is applied to the sensor. Forecasting bifurcations has been based on monitoring various system characteristics, such as noise-induced spectra [14], virtual Hopf phenomena [28], skewness of probability distributions [11] or flickering in bistable regions before bifurcations [2,6].…”

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confidence: 99%

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Forecasting bifurcation morphing: application to cantilever-based sensing

Lim

Epureanu

2011

Nonlinear Dyn

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Two novel techniques are proposed to enhance the bifurcation morphing method as applied to cantilever-based sensors. First, nonlinear feedback excitations with added time delay are employed to minimize the sensitivity of the sensors to small variations in the unavoidable time delay. Second, a novel approach to forecast bifurcations is applied to the sensors. This approach significantly reduces the time required to obtain bifurcation diagrams. Both techniques are demonstrated experimentally in detecting mass variations of a test cantilever beam. This cantileverbased sensor operating based on the bifurcation morphing method is shown to be accurate, quick and robust when these techniques are utilized.

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“…Reference [20] provides details regarding the use of λ to forecast bifurcations. In particular, Ref.…”

Section: Forecasting Bifurcationsmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Forecasting bifurcation morphing: application to cantilever-based sensing

Lim

Epureanu

2011

Nonlinear Dyn

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“…Van Nes and Scheffer [33] showed that, in six ecological models, recovery rates from small perturbations decrease as a regime shift was approached. For more on numerical and experimental approaches for detecting bifurcations before they occur by exploiting the critical slowing down phenomenon, we refer to Lim and Epureanu [34], Ghadami and Epureanu [35,36] and Van de Leemput et al [37].…”

Section: Alternative Measures and Topics For Future Researchmentioning

confidence: 99%

How to find simple nonlocal stability and resilience measures

Lundström

2018

Nonlinear Dyn

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Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena cannot be traced by the widespread local stability and resilience measures, based on linearizations, accounting only for arbitrary small perturbations. Using numerical estimates of the size and shape of the basin of attraction, as well as the systems returntime to the attractor after given a perturbation, we construct simple nonlocal stability and resilience measures that record a systems ability to tackle both large and small perturbations. We demonstrate our approach on the Solow-Swan model of economic growth, an electro-mechanical system, a stage-structured population model as well as on a highdimensional system, and conclude that the suggested measures detect dynamic behavior, crucial for a systems stability and resilience, which can be completely missed by local measures. The presented measures are also easy to implement on a standard laptop computer. We believe that our approach will constitute an important step toward filling a current gap in the literature by putting forward and explaining simple ideas and meth-N. L. P. Lundström (B) Department of Mathematics and Mathematical Statistics, Umeå University, 90187 Umeå, Sweden e-mail: niklas.lundstrom@umu.se ods, and by delivering explicit constructions of several promising nonlocal stability and resilience measures.

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Variance and Rate‐of‐Change as Early Warning Signals for a Critical Transition in an Aquatic Ecosystem State: A Test Case From Tasmania, Australia

et al. 2018

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Critical transitions in ecosystem states are often sudden and unpredictable. Consequently, there is a concerted effort to identify measurable early warning signals (EWS) for these important events. Aquatic ecosystems provide an opportunity to observe critical transitions due to their high sensitivity and rapid response times. Using palaeoecological techniques, we can measure properties of time series data to determine if critical transitions are preceded by any measurable ecosystem metrics, that is, identify EWS. Using a suite of palaeoenvironmental data spanning the last 2,400 years (diatoms, pollen, geochemistry, and charcoal influx), we assess whether a critical transition in diatom community structure was preceded by measurable EWS. Lake Vera, in the temperate rain forest of western Tasmania, Australia, has a diatom community dominated by Discostella stelligera and undergoes an abrupt compositional shift at ca. 820 cal yr BP that is concomitant with increased fire disturbance of the local vegetation. This shift is manifest as a transition from less oligotrophic acidic diatom flora (Achnanthidium minutissimum, Brachysira styriaca, and Fragilaria capucina) to more oligotrophic acidic taxa (Frustulia elongatissima, Eunotia diodon, and Gomphonema multiforme). We observe a marked increase in compositional variance and rate‐of‐change prior to this critical transition, revealing these metrics are useful EWS in this system. Interestingly, vegetation remains complacent to fire disturbance until after the shift in the diatom community. Disturbance taxa invade and the vegetation system experiences an increase in both compositional variance and rate‐of‐change. These trends imply an approaching critical transition in the vegetation and the probable collapse of the local rain forest system.

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Forecasting a class of bifurcations: Theory and experiment

Cited by 59 publications

References 34 publications

Forecasting bifurcation morphing: application to cantilever-based sensing

Forecasting bifurcation morphing: application to cantilever-based sensing

How to find simple nonlocal stability and resilience measures

Variance and Rate‐of‐Change as Early Warning Signals for a Critical Transition in an Aquatic Ecosystem State: A Test Case From Tasmania, Australia

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