Rate-induced transitions and advanced takeoff in power systems

Suchithra, K. S.; Gopalakrishnan, E. A.; Surovyatkina, Elena; Kurths, Jürgen

doi:10.1063/5.0002456

Cited by 15 publications

(12 citation statements)

References 28 publications

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“…duffle-like basins of attraction and fractality-induced tipping, as well as topological complexity of connections and interactions(Kasz á et al 2019;Suchithra et al 2020). …”

mentioning

confidence: 99%

Pattern Breaking: A Complex Systems Approach to Psychedelic Medicine

Hipólito¹,

Mago²,

Rosas³

et al. 2022

Preprint

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There is growing evidence for the safety and efficacy of psychedelic therapy in mental health care. What is less understood however, is how psychedelics act to yield therapeutic results. In this paper we propose that psychedelics act as destabilisers — both in a psychological and a neurophysiological sense. Our proposed framework builds on the ‘entropic brain’ hypothesis, according to which psychedelics increase the entropy of spontaneous cortical activity and, in parallel, the richness or depth of content of psychological experience. The so-called ‘RElaxed Beliefs Under pSychedelics’ (REBUS) model is a predictive-coding inspired extension to this hypothesis, which states that psychedelics’ entropic action is paralleled by a relaxation of prior assumptions. Here we adopt a complex systems theory (CST) perspective, proposing that psychedelics act as destabilisers of excessively reinforced fixed points — or ‘attractors’ — which translates as the breaking of excessively reinforced or overweighted patterns of thinking or behaving. Our CST approach explains how psychedelic-induced increases in brain entropy destabilise neurophysiological set-points that are synonymous with overweighted priors, thereby augmenting and enriching the account given by REBUS. We believe that this perspective helps inspire conceptualisations of psychedelic psychotherapy — bearing relevance both to the peak psychedelic experience and subsequent sub-acute period of potential recovery. We discuss implications for risk mitigation and treatment optimization in psychedelic medicine.

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“…duffle-like basins of attraction and fractality-induced tipping, as well as topological complexity of connections and interactions(Kasz á et al 2019;Suchithra et al 2020). …”

mentioning

confidence: 99%

Pattern Breaking: A Complex Systems Approach to Psychedelic Medicine

Hipólito¹,

Mago²,

Rosas³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…5 Rate-induced tipping in power grid networks R-tipping instabilities are not confined to natural systems, but can occur in any system, including human systems. One example is the energy sector and power grid networks (Suchithra et al, 2020). Crucially, electricity needs to be used as soon as it is produced since it cannot be stored easily (Mokrian et al, 2006).…”

Section: Rate-induced Tipping In Ecology and Climatementioning

confidence: 99%

Rate-induced tipping in natural and human systems

Ritchie

Alkhayuon

Cox

et al. 2022

Preprint

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Abstract. Over the last two decades, tipping points have become a hot topic due to the devastating consequences that they may have on natural and human systems. Tipping points are typically associated with a system bifurcation when external forcing crosses a critical level, causing an abrupt transition to an alternative, and often less desirable, state. The main message of this review is that the rate of change in forcing is arguably of even greater relevance in the human-dominated anthropocene, but is rarely examined as a potential sole mechanism for tipping points. Thus, we address the related phenomenon of rate-induced tipping: an instability that occurs when external forcing varies across some critical rate, usually without crossing any bifurcations. First, we explain when to expect rate-induced tipping. Then, we use three illustrating examples of differing complexity to highlight universal and generic properties of rate-induced tipping in a range of natural and human systems.

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“…The focus of this work is on systems that are particularly sensitive to how fast the external input changes [53]. Such systems may not even have any critical levels, but they may have critical rates of change: they suddenly and unexpectedly move to a different state if the external input changes too fast [79,100,116,10,104,5,113,80,55,108,66,7,87,20,75,83]. Although critical rates are less understood than critical levels, they are equally relevant and ubiquitous.…”

Section: Motivation: Critical Factors and R-tippingmentioning

confidence: 99%

Rate-Induced Tipping: Thresholds, Edge States and Connecting Orbits

Wieczorek¹,

Xie²,

Ashwin³

2021

Preprint

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Rate-induced tipping, or simply R-tipping, occurs when time-variation of input parameters of a dynamical system interacts with system timescales to give genuine nonautonomous instabilities that cannot, in general, be understood in terms of autonomous bifurcations in the frozen system with a fixed-in-time input. Such instabilities appear as the input varies at some critical rates. Finding these critical rates and characterising what happens when they are exceeded is of great interest in natural science. The challenge is that it requires development of mathematical concepts and techniques beyond classical autonomous bifurcation theory.This paper develops an accessible mathematical framework and gives testable criteria for R-tipping in multidimensional nonautonomous dynamical systems with an autonomous future limit. Our focus is on R-tipping via loss of tracking of base attractors that are equilibria in the frozen system, due to crossing what we call regular thresholds. These thresholds are associated with regular edge states: compact hyperbolic invariant sets with one unstable direction and orientable stable manifold, that lie on a basin boundary in the frozen system. We define Rtipping and critical rates for the nonautonomous system in terms of special solutions that limit to a compact invariant set of the future limit system that is not an attractor. We then focus on the case when the limit set is a regular edge state of the future limit system, which we call the regular R-tipping edge state that anchors the associated regular R-tipping threshold at infinity. We then introduce the concept of edge tails to rigorously classify R-tipping into reversible, irreversible and degenerate cases. The main idea is to use autonomous dynamics and regular edge states of the future limit system to analyse R-tipping in the nonautonomous system. To that end, we compactify the original nonautonomous system to include the limiting autonomous dynamics. This allows us to give easily verifiable conditions in terms of simple properties of the frozen system and input variation that are sufficient for the occurrence of Rtipping. Additionally, we give necessary and sufficient conditions for the occurrence of reversible and irreversible R-tipping in terms of computationally verifiable (heteroclinic) connections to regular R-tipping edge states in the compactified system. Thus, our work extends existing results for R-tipping in one dimension to arbitrary dimension and to different cases of R-tipping, some of which can occur only in higher dimensions.

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Rate-induced transitions and advanced takeoff in power systems

Cited by 15 publications

References 28 publications

Pattern Breaking: A Complex Systems Approach to Psychedelic Medicine

Pattern Breaking: A Complex Systems Approach to Psychedelic Medicine

Rate-induced tipping in natural and human systems

Rate-Induced Tipping: Thresholds, Edge States and Connecting Orbits

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