Delay Embeddings for Forced Systems. II. Stochastic Forcing

No abstract is available for this paper.

• Publication year

  2003

• Venue

  Journal of nonlinear science

• Publication date

  2003-12-03

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1007/s00332-003-0534-4
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Random Dynamical Systems

  2003cited by this paper
• For Differential Equations with r Parameters, 2r+1 Experiments Are Enough for Identification

  2001cited by this paper
• Delay Embeddings for Forced Systems. I. Deterministic Forcing

  1999influential reference
• Takens embedding theorems for forced and stochastic systems

  1997cited by this paper
• Orders of Input/Output Differential Equations and State-Space Dimensions

  1995cited by this paper
• Modelling and analysis of non-linear time series

  1989cited by this paper
• Fractals everywhere

  1988cited by this paper
• Random Perturbations of Dynamical Systems

  1988cited by this paper
• Input-output parametric models for non-linear systems Part II: stochastic non-linear systems

  1985cited by this paper
• GENERIC OBSERVABILITY OF DIFFERENTIABLE SYSTEMS

  1981cited by this paper
• Polynomial Response Maps

  1979cited by this paper
• Realization Theory of Discrete-Time Nonlinear Systems: Part I - The Bounded Case

  1979cited by this paper
• Calculus on Vector Bundles

  1975cited by this paper
• A setting for global analysis

  1966cited by this paper
• Transversality in manifolds of mappings

  1963cited by this paper

• Wasserstein Geometry of Information Loss in Nonlinear Dynamical Systems

  2026cites this paper
• Smooth embeddings in contracting recurrent networks driven by regular dynamics: A synthesis for neural representation

  2026cites this paper
• Inference of hidden common driver dynamics by anisotropic self-organizing neural networks

  2025cites this paper
• Empirical dynamic modeling for prediction and control of pest populations

  2025cites this paper
• Investigation of Fast Topological Data Analysis Feature Extraction for High-Rate Dynamic Prediction

  2025cites this paper
• In search for the invisible: motor inhibition in monkey premotor cortex and its RNN replicas

  2025cites this paper
• Correlation Dimension of Auto-Regressive Large Language Models

  2025cites this paper
• Learning Iterated Function Systems from Time Series of Partial Observations

  2025influential citation
• Learning Koopman Models From Data Under General Noise Conditions

  2025influential citation
• Refuting causal relations for synchronized pathogen dynamics

  2025cites this paper
• Linearizing and forecasting: a reservoir computing route to digital twins of the brain

  2025cites this paper
• Causal-oriented representation learning for time-series forecasting based on the spatiotemporal information transformation

  2025cites this paper
• Real-time state estimation of nonstationary systems through dominant fundamental frequency using topological data analysis features

  2025cites this paper
• FRIREN: Beyond Trajectories - A Spectral Lens on Time

  2025cites this paper
• Climatic drivers of infectious diarrheal disease epidemics in China: an empirical dynamic modeling analysis of 21 million cases.

  2025cites this paper
• Reconstructing and predicting stochastic dynamical systems using probabilistic deep learning.

  2025cites this paper
• Measure-Theoretic Time-Delay Embedding

  2024cites this paper
• Empirical dynamic programming for model‐free ecosystem‐based management

  2024cites this paper
• Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks.

  2024cites this paper
• Data-driven discovery of chemotactic migration of bacteria via coordinate-invariant machine learning

  2024cites this paper
• Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems

  2024cites this paper
• Learning from the past: reservoir computing using delayed variables

  2024cites this paper
• Real-time state estimation using recurrent neural network and topological data analysis

  2024cites this paper
• Predicting dynamical systems with too few time-delay measurements: Error estimates

  2024cites this paper
• Explaining empirical dynamic modelling using verbal, graphical and mathematical approaches

  2024cites this paper
• VR Sickness Evaluation Method Using Recurrence Period Density Entropy

  2024cites this paper
• Optimal Reconstruction of Vector Fields from Data for Prediction and Uncertainty Quantification

  2024cites this paper
• State space reconstruction of Markov chains via autocorrelation structure

  2024cites this paper
• Quantifying interactions in the water-energy-food nexus: data-driven analysis utilizing a causal inference method

  2024cites this paper
• Data-driven dimensionality reduction and causal inference for spatiotemporal climate fields.

  2023cites this paper
• Effects of climate change on vegetation dynamics of the Qinghai-Tibet Plateau, a causality analysis using empirical dynamic modeling

  2023cites this paper
• A Markovian dynamics for Caenorhabditis elegans behavior across scales

  2023cites this paper
• Refuting Causal Relations in Epidemiological Time Series

  2023cites this paper
• Revealing system dimension from single-variable time series.

  2023cites this paper
• Multistep Ahead Prediction of Vehicle Lateral Dynamics Based on Echo State Model

  2023cites this paper
• Equivariant embedding of finite-dimensional dynamical systems

  2023cites this paper
• Geometric constraints improve inference of sparsely observed stochastic dynamics

  2023cites this paper
• Universal window size-dependent transition of correlations in complex systems.

  2023cites this paper
• Learned Reconstruction of Protein Folding Trajectories from Noisy Single-Molecule Time Series.

  2023cites this paper
• Data assimilation with hybrid modeling

  2023cites this paper
• Fluctuating landscapes and heavy tails in animal behavior

  2023cites this paper
• Multi-step ahead state estimation with hybrid algorithm for high-rate dynamic systems

  2023cites this paper
• Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

  2022cites this paper
• Prediction of dynamical systems from time-delayed measurements with self-intersections

  2022cites this paper
• Deep learning delay coordinate dynamics for chaotic attractors from partial observable data

  2022cites this paper
• Embedding entropy: a nonlinear measure of dynamical causality

  2022cites this paper
• Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

  2022cites this paper
• Ensemble of long short-term memory recurrent neural network for semi-active control of tuned liquid wall damper

  2022cites this paper
• Predicting Latent States of Dynamical Systems With State-Space Reconstruction and Gaussian Processes

  2022cites this paper
• Data-driven Discovery of Chemotactic Migration of Bacteria via Machine Learning

  2022cites this paper
• Recent developments in empirical dynamic modelling

  2022cites this paper
• Random errors are neither: On the interpretation of correlated data

  2022cites this paper
• Rethinking the Prevalence and Relevance of Chaos in Ecology

  2022cites this paper
• Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

  2022cites this paper
• Renormalization group approach to connect discrete- and continuous-time descriptions of Gaussian processes.

  2021cites this paper
• Multi-Time Resolution Ensemble LSTMs for Enhanced Feature Extraction in High-Rate Time Series

  2021cites this paper
• Beyond linearity, stability, and equilibrium: The edm package for empirical dynamic modeling and convergent cross-mapping in Stata

  2021cites this paper
• Reconstructing common latent input from time series with the mapper-coach network and error backpropagation

  2021cites this paper
• On the Shroer–Sauer–Ott–Yorke Predictability Conjecture for Time-Delay Embeddings

  2021cites this paper
• Morphodynamical cell state description via live-cell imaging trajectory embedding

  2021cites this paper
• Maximally predictive ensemble dynamics from data

  2021cites this paper
• Real-Time Machine Learning for High-Rate Structural Health Monitoring

  2021cites this paper
• Relaxation of Some Confusions about Confounders

  2021cites this paper
• Reconstructing shared dynamics with a deep neural network

  2021cites this paper
• Maximally predictive states: From partial observations to long timescales.

  2021cites this paper
• Reconstruction of protein structures from single-molecule time series.

  2020cites this paper
• Forecasting unprecedented ecological fluctuations

  2020cites this paper
• International Federation of Clinical Neurophysiology (IFCN) - EEG research workgroup: Recommendations on frequency and topographic analysis of resting state EEG rhythms. Part 1: Applications in clinical research studies.

  2020cites this paper
• Capturing the continuous complexity of behaviour in Caenorhabditis elegans

  2020cites this paper
• Mean local autocovariance provides robust and versatile choice of delay for reconstruction using frequently sampled flowlike data.

  2020cites this paper
• A mobile ELF4 delivers circadian temperature information from shoots to roots

  2020cites this paper
• Partial cross mapping eliminates indirect causal influences

  2020cites this paper
• Information dynamics with confidence: Using reservoir computing to construct confidence intervals for information-dynamic measures.

  2019cites this paper
• Capturing the Continuous Complexity of Behavior in C. elegans

  2019cites this paper
• Partial Observations and Conservation Laws: Gray-Box Modeling in Biotechnology and Optogenetics

  2019cites this paper
• A mobile ELF4 delivers circadian temperature information from shoots to roots

  2019cites this paper
• A Geometric Approach to the Transport of Discontinuous Densities

  2019cites this paper
• Approximate Bayesian computation with the Wasserstein distance

  2019influential citation
• On the structure of time-delay embedding in linear models of non-linear dynamical systems.

  2019cites this paper
• Reservoir Transfer on Analog Neuromorphic Hardware

  2019cites this paper
• Hidden similarities in the dynamics of a weakly synchronous marine metapopulation

  2019cites this paper
• Reconstructing latent dynamical noise for better forecasting observables.

  2018cites this paper
• Topological recognition of critical transitions in time series of cryptocurrencies

  2018cites this paper
• Nonlinear dynamics and noise in fisheries recruitment: A global meta-analysis

  2018cites this paper
• Twenty years after “The Impact of Chaos”: what have been achieved and what should be answered

  2018cites this paper
• Information-theoretic model selection for optimal prediction of stochastic dynamical systems from data.

  2018cites this paper
• Minimising the Kullback–Leibler Divergence for Model Selection in Distributed Nonlinear Systems

  2018influential citation
• A probabilistic Takens theorem

  2018cites this paper
• Manifold learning for organizing unstructured sets of process observations.

  2018cites this paper
• Convergent Cross Mapping: Theory and an Example

  2018cites this paper
• Randomly distributed embedding making short-term high-dimensional data predictable

  2018cites this paper
• Recovery of Protein Folding Funnels from Single-Molecule Time Series by Delay Embeddings and Manifold Learning.

  2018cites this paper
• Input space dependent controller for civil structures exposed to multi-hazard excitations

  2018cites this paper
• Real-Time Variable Multidelay Controller for Multihazard Mitigation

  2018influential citation
• Inference in generative models using the Wasserstein distance

  2017cites this paper
• Circumventing structural uncertainty: A Bayesian perspective on nonlinear forecasting for ecology

  2017cites this paper
• Predicting coastal algal blooms in southern California.

  2017cites this paper
• Detecting causality from short time-series data based on prediction of topologically equivalent attractors

  2017cites this paper
• Variable input observer for structural health monitoring of high-rate systems

  2017cites this paper
• Data-based prediction and causality inference of nonlinear dynamics

  2017cites this paper