Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Elastic Collisions: Case Study01:15

Elastic Collisions: Case Study

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Design Example: Analyzing Capacity Contours for Flood Risk Assessment01:17

Design Example: Analyzing Capacity Contours for Flood Risk Assessment

Flood risk assessment involves careful planning and analysis to ensure the safety of communities near water retention structures. Capacity contours are a vital tool in this process, as they illustrate the potential spread of water at specific levels in a given area. In the context of building a bund across a small valley, these contours play a critical role in evaluating the safety of nearby residential areas.In this example, the bund is intended to store stormwater in the valley. The engineers...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
The Squeeze Theorem01:30

The Squeeze Theorem

Certain mathematical functions exhibit unpredictable or highly variable behavior near specific input values, making direct evaluation of their limits challenging. This complexity may arise from rapid oscillations or irregular patterns that obscure the function’s trend. In such cases, the Squeeze Theorem offers a reliable method for determining limits.According to the Squeeze Theorem, if a function is confined between two other functions near a particular point, and both outer functions approach...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Chaotic ghosts in systems with parameter drift: Delay and control critical transitions.

Physical review. E·2026
Same author

Multiscale spatiotemporal neural network with multi-attention mechanism using brain partitioning for motor imagery recognition.

Journal of neuroscience methods·2026
Same author

Complex bifurcation structures in a Hodgkin-Huxley model of thermally sensitive neurons under periodic perturbation.

Physical review. E·2025
Same author

Adaptive Whole-Brain Dynamics Predictive Method: Relevancy to Mental Disorders.

Research (Washington, D.C.)·2025
Same author

Unsupervised Domain Adaptation With Synchronized Self-Training for Cross- Domain Motor Imagery Recognition.

IEEE journal of biomedical and health informatics·2025
Same author

Transcriptomic Evidence Reveals the Dysfunctional Mechanism of Synaptic Plasticity Control in ASD.

Genes·2025
Same journal

Erratum: Spectroscopy and Ground-State Transfer of Ultracold Bosonic ^{39}K^{133}Cs Molecules [Phys. Rev. Lett. 135, 203401 (2025)].

Physical review letters·2026
Same journal

Erratum: Lifetime of the ^{2}F_{7/2} Level in Yb^{+} for Spontaneous Emission of Electric Octupole Radiation [Phys. Rev. Lett. 127, 213001 (2021)].

Physical review letters·2026
Same journal

Laser-Plasma Based Seeded Free Electron Laser in the High-Gain Regime.

Physical review letters·2026
Same journal

Parent Hamiltonians for Stabilizer Quantum Many-Body Scars.

Physical review letters·2026
Same journal

Properties of Heavy Cosmic Nuclei Phosphorus, Chlorine, Argon, Potassium, and Calcium: Results from the Alpha Magnetic Spectrometer.

Physical review letters·2026
Same journal

Role of Spin-Isospin Symmetries in Nuclear β-Decays.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: Jun 2, 2026

Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

Predicting catastrophes in nonlinear dynamical systems by compressive sensing.

Wen-Xu Wang1, Rui Yang, Ying-Cheng Lai

  • 1School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA. wenxuw@gmail.com

Physical Review Letters
|May 17, 2011
PubMed
Summary
This summary is machine-generated.

Predicting system catastrophes is now possible even without knowing the exact equations. This new method uses time series data and compressive sensing to forecast major events in nonlinear dynamical systems.

More Related Videos

Automated Analysis of Dynamic Ca2+ Signals in Image Sequences
06:49

Automated Analysis of Dynamic Ca2+ Signals in Image Sequences

Published on: June 16, 2014

Related Experiment Videos

Last Updated: Jun 2, 2026

Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

Automated Analysis of Dynamic Ca2+ Signals in Image Sequences
06:49

Automated Analysis of Dynamic Ca2+ Signals in Image Sequences

Published on: June 16, 2014

Area of Science:

  • Nonlinear dynamics
  • Complex systems analysis
  • Predictive modeling

Background:

  • Predicting catastrophic events in complex systems is a critical challenge.
  • Traditional methods often require complete knowledge of system equations, which is frequently unavailable.
  • Time series data is often the only accessible information for real-world systems.

Purpose of the Study:

  • To develop a general approach for predicting catastrophes in nonlinear dynamical systems.
  • To enable prediction when system equations are unknown, relying solely on time series data.
  • To demonstrate the efficacy of the proposed method using chaotic systems.

Main Methods:

  • Expanding the unknown vector field or map of the dynamical system into a function series.
  • Utilizing compressive sensing techniques to accurately estimate the coefficients of the function series.
  • Applying the method to paradigmatic chaotic systems for validation.

Main Results:

  • Successfully demonstrated a method for predicting system behavior from time series data alone.
  • Accurate estimation of system dynamics was achieved using compressive sensing.
  • The approach proved effective in forecasting potential catastrophes in tested chaotic systems.

Conclusions:

  • The proposed method offers a viable approach to predicting catastrophes in unknown nonlinear dynamical systems.
  • Compressive sensing is a powerful tool for reconstructing system dynamics from limited time series data.
  • This work advances the field of predictive modeling for complex systems.