A mathematical framework for critical transitions: bifurcations, fast-slow systems and stochastic dynamics

DOI10.1016/j.physd.2011.02.012zbMath1225.35242arXiv1101.2899OpenAlexW2168773352MaRDI QIDQ2276145

Christian Kuehn

Publication date: 1 August 2011

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.2899

zbMATH Keywords

Fokker-Planck equationstochastic dynamicsbifurcation delaymultiple time scalescritical transitiontipping point

Mathematics Subject Classification ID

Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Fokker-Planck equations (35Q84)

Related Items

Statistical mechanics and information-theoretic perspectives on complexity in the Earth system, Spatial early warning signals for tipping points using dynamic mode decomposition, On the effect of forcing on fold bifurcations and early-warning signals in population dynamics, Predicting critical in a model of systemic inflammation, Stability and Bifurcation of a Class of Stochastic Closed Orbit Equations, Synchronized Oscillatory Dynamics for a 1-D Model of Membrane Kinetics Coupled by Linear Bulk Diffusion, On using extreme values to detect global stability thresholds in multi-stable systems: the case of transitional plane Couette flow, A mathematical framework for critical transitions: normal forms, variance and applications, A paradigmatic system to study the transition from zero/Hopf to double-zero/Hopf bifurcation, Rate-induced tipping from periodic attractors: Partial tipping and connecting orbits, Several indicators of critical transitions for complex diseases based on stochastic analysis, How stochasticity influences leading indicators of critical transitions, Topography of cyclopropyl radical ring opening to allyl radical on the CASSCF(3,3) surface: Valley-ridge inflection points by Newton trajectories, Continuation of probability density functions using a generalized Lyapunov approach, Rate-Induced Tipping in Heterogeneous Reaction-Diffusion Systems: An Invariant Manifold Framework and Geographically Shifting Ecosystems, Analysis and modelling of glacial climate transitions using simple dynamical systems, Predictions of critical transitions with non-stationary reduced order models, Patterned vegetation, tipping points, and the rate of climate change, Rate-induced tipping: thresholds, edge states and connecting orbits, Hunting French ducks in a noisy environment, A Predator--2 Prey Fast--Slow Dynamical System for Rapid Predator Evolution, Early warnings indicators of financial crises via auto regressive moving average models, Limits to predictability of the asymptotic state of the Atlantic meridional overturning circulation in a conceptual climate model, The role of conceptual models in climate research, The role of slow system dynamics in predicting the degeneracy of slow invariant manifolds: the case of vdP relaxation-oscillations, Early-warning signs for pattern-formation in stochastic partial differential equations, Qualitative Analysis of Critical Transitions in Complex Disease Propagation from a Dynamical Systems Perspective, A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells, Recurrence analysis of slow–fast systems, Critical transitions and early warning signals in repeated cooperation games, Noise-induced tipping under periodic forcing: Preferred tipping phase in a non-adiabatic forcing regime, Random attractions and bifurcation for the classical Rayleigh-Van der Pol equations with small noise, Time-dependent saddle-node bifurcation: breaking time and the point of no return in a non-autonomous model of critical transitions, Moment-closure approximations for discrete adaptive networks, When panic makes you blind: a chaotic route to systemic risk, How noise and coupling influence leading indicators of population extinction in a spatially extended ecological system, Non-equilibrium transitions in multiscale systems with a bifurcating slow manifold, Response theory and phase transitions for the thermodynamic limit of interacting identical systems, Stability and bifurcation of two-dimensional stochastic differential equations with multiplicative excitations, Critical Transition Analysis of the Deterministic Wind-Driven Ocean Circulation — A Flux-Based Network Approach, Earth’s carbon cycle: A mathematical perspective, Timing and shape of stochastic autocatalytic burst formation, Critical transitions in a model of a genetic regulatory system, Predicting critical transitions in multiscale dynamical systems using reservoir computing, Edge states in the climate system: exploring global instabilities and critical transitions, Tipping Phenomena and Points of No Return in Ecosystems: Beyond Classical Bifurcations, A Fast-Slow Dynamical System Model of Addiction: Predicting Relapse Frequency, Fast basin stability estimation for dynamic systems under large perturbations with sequential support vector machine, Introduction to the special issue on the statistical mechanics of climate, Detecting regime transitions in time series using dynamic mode decomposition, Bifurcation dodge: avoidance of a thermoacoustic instability under transient operation, Transition to blow-up in a reaction–diffusion model with localized spike solutions, On some aspects of the response to stochastic and deterministic forcings, Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems, Dynamics and absorption properties of stochastic equations with Hölder diffusion coefficients

Cites Work

• Hunting French ducks in a noisy environment
• Multiple time scale dynamics
• Evaluation of conditional Wiener integrals by numerical integration of stochastic differential equations
• On the noise-induced passage through an unstable periodic orbit. I: Two-level model
• Noise-induced transitions. Theory and applications in physics, chemistry, and biology
• Stochastic methods. A handbook for the natural and social sciences
• On stability loss delay for dynamical bifurcations
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Asymptotic methods for relaxation oscillations and applications
• Applications of centre manifold theory
• Geometric singular perturbation theory for ordinary differential equations
• Differential equations with small parameters and relaxation oscillations. Translation from the Russian by F. M. C. Goodspeed
• Duck-shaped solutions and winding.
• Bifurcations and dynamics of spiral waves
• Normally hyperbolic invariant manifolds in dynamical systems
• A stochastic Hopf bifurcation
• Attractors for random dynamical systems
• Statistical inference for ergodic diffusion processes.
• Random attractors -- general properties, existence and applications to stochastic bifurcation theory
• Pathwise description of dynamic pitchfork bifurcations with additive noise
• The Fokker-Planck equation. Methods of solutions and applications.
• Geometric singular perturbation theory for stochastic differential equations.
• Probability densities for noisy delay bifurcations
• Invariant manifolds for random dynamical systems with slow and fast variables
• Critical slowing down in one-dimensional maps and beyond
• Self-induced stochastic resonance in excitable systems
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• Extending slow manifolds near transcritical and pitchfork singularities
• Mixed-Mode Oscillations with Multiple Time Scales
• Tipping elements in the Earth's climate system
• Pattern Formation
• Singular Hopf Bifurcation in Systems with Two Slow Variables
• Stability of dynamical systems
• On the Classification of Dynamical Systems
• The Slow Passage through a Hopf Bifurcation: Delay, Memory Effects, and Resonance
• METASTABILITY IN SIMPLE CLIMATE MODELS: PATHWISE ANALYSIS OF SLOWLY DRIVEN LANGEVIN EQUATIONS
• Tracking Invariant Manifolds up to Exponentially Small Errors
• Canard cycles and center manifolds
• Noise-Induced Phenomena in Slow-Fast Dynamical Systems
• Horseshoes in the forced van der Pol system
• Chaos
• Stochastic bifurcation
• Elements of applied bifurcation theory
• Canards in \(\mathbb{R}^3\)
• Stochastic differential equations. An introduction with applications.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item