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

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...
Feedback control systems01:26

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
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...
Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

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

Related Experiment Video

Updated: May 18, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Forecasting the future: is it possible for adiabatically time-varying nonlinear dynamical systems?

Rui Yang1, Ying-Cheng Lai, Celso Grebogi

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

Chaos (Woodbury, N.Y.)
|October 2, 2012
PubMed
Summary
This summary is machine-generated.

Forecasting time-dependent nonlinear dynamical systems is now possible using compressive sensing. This method predicts future states and attractors from limited time-series data, even when system equations are unknown.

Related Experiment Videos

Last Updated: May 18, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

  • Nonlinear dynamics
  • Time series analysis
  • Compressive sensing

Background:

  • Real-world dynamical systems are subject to time-varying environmental influences.
  • Assessing system sustainability and performance requires forecasting future states and attractors from time-series data.
  • Forecasting is challenging for systems with unknown governing equations.

Purpose of the Study:

  • To propose a method for forecasting the future states and attractors of nonlinear dynamical systems with time-dependent environmental influences.
  • To demonstrate the application of the compressive-sensing paradigm to this forecasting problem.
  • To provide a tool for assessing the sustainability of natural and man-made systems.

Main Methods:

  • Formulating the forecasting problem within the compressive sensing framework.
  • Utilizing a series expansion in both dynamical and time variables.
  • Solving the forecasting problem using only a few measurements from the time series.

Main Results:

  • A viable solution is presented for forecasting time-dependent nonlinear dynamical systems using compressive sensing.
  • The method enables accurate forecasting even when the system's equations are unknown.
  • The approach relies on a series expansion and limited time-series measurements.

Conclusions:

  • The proposed compressive-sensing approach offers a powerful method for forecasting nonlinear dynamical systems under environmental influences.
  • This technique is valuable for predicting system behavior and assessing sustainability.
  • The method's effectiveness is demonstrated for systems with unknown dynamics.