Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue

Feudel, Ulrike; Pisarchik, Alexander N.; Showalter, Kenneth

doi:10.1063/1.5027718

Cited by 113 publications

(66 citation statements)

References 110 publications

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“…Bistable ecosystems can go through state transitions, or regime shifts [81], in various ways, including a passage through a bifurcation point (B-tipping), as a result of environmental fluctuations (N-tipping), or as a result of fastly varying environmental conditions (R-tipping) [82,83]. Such transitions are generally discussed as whole-system responses, occurring simultaneously at all points in space.…”

Section: Front Dynamicsmentioning

confidence: 99%

Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous?

et al. 2019

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Understanding ecosystem response to drier climates calls for modeling the dynamics of dryland plant populations, which are crucial determinants of ecosystem function, as they constitute the basal level of whole food webs. Two modeling approaches are widely used in population dynamics, individual (agent)-based models and continuum partial-differential-equation (PDE) models. The latter are advantageous in lending themselves to powerful methodologies of mathematical analysis, but the question of whether they are suitable to describe small discrete plant populations, as is often found in dryland ecosystems, has remained largely unaddressed. In this paper, we first draw attention to two aspects of plants that distinguish them from most other organisms-high phenotypic plasticity and dispersal of stress-tolerant seeds-and argue in favor of PDE modeling, where the state variables that describe population sizes are not discrete number densities, but rather continuous biomass densities. We then discuss a few examples that demonstrate the utility of PDE models in providing deep insights into landscape-scale behaviors, such as the onset of pattern forming instabilities, multiplicity of stable ecosystem states, regular and irregular, and the possible roles of front instabilities in reversing desertification. We briefly mention a few additional examples, and conclude by outlining the nature of the information we should and should not expect to gain from PDE model studies.

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Section: Front Dynamicsmentioning

confidence: 99%

Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous?

et al. 2019

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“…The phenomenon of a stable equilibrium losing its stability as a slowly varying control parameter or some external forcing passes some critical value (tipping point) is referred to as a critical transition [1][2][3][4][5][6][7][8][9][10][11] . A critical transition can be heralded by the phenomenon of critical slowing down (CSD), an increasingly slow recovery from small perturbations.…”

Section: Introductionmentioning

confidence: 99%

No evidence for critical slowing down prior to human epileptic seizures

Wilkat

Rings

Lehnertz

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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There is a ongoing debate whether generic early warning signals for critical transitions exist that can be applied across diverse systems. The human epileptic brain is often considered as a prototypical system, given the devastating and, at times, even life-threatening nature of the extreme event epileptic seizure. More than three decades of international effort has successfully identified predictors of imminent seizures. However, the suitability of typically applied early warning indicators for critical slowing down, namely variance and lag-1 autocorrelation, for indexing seizure susceptibility is still controversially discussed. Here, we investigated long-term, multichannel recordings of brain dynamics from 28 subjects with epilepsy. Using a surrogate-based evaluation procedure of sensitivity and specificity of time-resolved estimates of early warning indicators, we found no evidence for critical slowing down prior to 105 epileptic seizures.

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“…The goal of this letter is to explore, using a simplified yet Earth-like climate model, the phase space of the climate system by taking advantage of the rich dynamics resulting from adding stochastic perturbations, and, in particular, by focusing on noise-induced transitions between the warm (W) and snowball (SB) attractors and linking this with the global stability properties analysed in [9] using tools and ideas of highdimensional deterministic dynamical systems. The methodology proposed here is of general relevance for studying multistable systems [10] and, specifically, for studying in a novel way the properties of the Earth tipping elements [11].…”

mentioning

confidence: 99%

“…Multistable systems are extensively investigated both in natural and social sciences [10] and they can be introduced as follows. We consider a smooth autonomous continuoustime dynamical system acting on a smooth finite-dimensional compact manifold M. We define x(t, x 0 )=S t (x 0 ) as an orbit at time t, where S t is the evolution operator, and x 0 the initial conditions at t = 0.…”

mentioning

confidence: 99%

Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View

2019

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The Earth is well-known to be, in the current astronomical configuration, in a regime where two asymptotic states can be realised. The warm state we live in is in competition with the ice-covered snowball state. The bistability exists as a result of the positive ice-albedo feedback. In a previous investigation performed on a intermediate complexity climate model we have identified the unstable climate states (Melancholia states) separating the co-existing climates, and studied their dynamical and geometrical properties. The Melancholia states are ice-covered up to the mid-latitudes and attract trajectories initialised on the basins boundary. In this paper, we study how stochastically perturbing the parameter controlling the intensity of the incoming solar radiation impacts the stability of the climate. We detect transitions between the warm and the snowball state and analyse in detail the properties of the noise-induced escapes from the corresponding basins of attraction. We determine the most probable paths for the transitions and find evidence that the Melancholia states act as gateways, similarly to saddle points in an energy landscape. arXiv:1808.05098v2 [physics.ao-ph]

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Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue

Cited by 113 publications

References 110 publications

Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous?

Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous?

No evidence for critical slowing down prior to human epileptic seizures

Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View

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