A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

Hunting French ducks in a noisy environment

(2012) Nils Berglund et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Quantifying limits to detection of early warning for critical transitions

(2012) C. Boettiger et al.   Journal of the Royal Society Interface

Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh–Nagumo model

(2012) Nils Berglund et al.   NONLINEARITY

Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system

(2012) P. Ashwin et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Time-scale and noise optimality in self-organized critical adaptive networks

(2012) Christian Kuehn   PHYSICAL REVIEW E

Scaling Effects and Spatio-Temporal Multilevel Dynamics in Epileptic Seizures

(2012) Christian Meisel et al.   PLoS One

Mixed-Mode Oscillations with Multiple Time Scales

(2012) Mathieu Desroches et al.   SIAM REVIEW

Slowing Down in Spatially Patterned Ecosystems at the Brink of Collapse

(2011) Vasilis Dakos et al.   AMERICAN NATURALIST

A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics

(2011) Christian Kuehn   PHYSICA D-NONLINEAR PHENOMENA

Regime shifts in ecological systems can occur with no warning

(2010) Alan Hastings et al.   ECOLOGY LETTERS

Tipping points: Early warning and wishful thinking

(2010) Peter D. Ditlevsen et al.   GEOPHYSICAL RESEARCH LETTERS

Climate tipping as a noisy bifurcation: a predictive technique

(2010) J. M. T. Thompson et al.   IMA JOURNAL OF APPLIED MATHEMATICS

EARLY WARNINGS FOR CATASTROPHIC SHIFTS IN ECOSYSTEMS: COMPARISON BETWEEN SPATIAL AND TEMPORAL INDICATORS

(2010) RAUL DONANGELO et al.   INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Periodic orbits and chaos in fast–slow systems with Bogdanov–Takens type fold points

(2010) Hayato Chiba   JOURNAL OF DIFFERENTIAL EQUATIONS

Early warning signals of extinction in deteriorating environments

(2010) John M. Drake et al.   NATURE

Early-warning signals for critical transitions

(2009) Marten Scheffer et al.   NATURE

Spatial correlation as leading indicator of catastrophic shifts

(2009) Vasilis Dakos et al.   Theoretical Ecology

Random Perturbations of Canards

(2008) Richard B. Sowers   JOURNAL OF THEORETICAL PROBABILITY

Influence of the event magnitude on the predictability of an extreme event

(2008) S. Hallerberg et al.   PHYSICAL REVIEW E

Slowing down as an early warning signal for abrupt climate change

(2008) V. Dakos et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Tipping elements in the Earth's climate system

(2008) T. M. Lenton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example

(2008) Martin Krupa et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS