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

Plotting and Calibrating the Root Locus01:19

Plotting and Calibrating the Root Locus

433
Root loci often diverge as system poles shift from the real axis to the complex plane. Key points in this transition are the breakaway and break-in points, indicating where the root locus leaves and reenters the real axis. The branches of the root locus form an angle of 180/n degrees with the real axis, where n is the number of branches at a breakaway or break-in point.
The maximum gain occurs at the breakaway points between open-loop poles on the real axis, while the minimum gain is...
433
SFG Algebra01:16

SFG Algebra

316
In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
316
Linear time-invariant Systems01:23

Linear time-invariant Systems

872
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...
872
Stability01:28

Stability

384
The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
384
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

357
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....
357
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

345
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,...
345

You might also read

Related Articles

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

Sort by
Same author

The recipe of a four-dimensional pastry: The hypercake.

Chaos (Woodbury, N.Y.)·2026
Same author

Inference of couplings between variables of a given system using causal wavelets, causal information, equations reconstruction, and other techniques.

Chaos (Woodbury, N.Y.)·2025
Same author

Optimal placement of sensor and actuator for controlling low-dimensional chaotic systems based on global modeling.

Chaos (Woodbury, N.Y.)·2023
Same author

COVID-19 in Africa: Underreporting, demographic effect, chaotic dynamics, and mitigation strategy impact.

PLoS neglected tropical diseases·2022
Same author

Chaos theory applied to the outbreak of COVID-19: an ancillary approach to decision making in pandemic context.

Epidemiology and infection·2020

Related Experiment Video

Updated: Jan 16, 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

501

Structure analysis of the Lorenz-84 chaotic attractor.

M Rosalie1, S Mangiarotti2

  • 1Université de Perpignan Via Domitia, CNRS, Laboratoire Génome et Développement des Plantes UMR-5096, F-66860 Perpignan, France.

Chaos (Woodbury, N.Y.)
|October 1, 2025
PubMed
Summary

Researchers explored the Lorenz-84 attractor

More Related Videos

C. elegans Tracking and Behavioral Measurement
07:36

C. elegans Tracking and Behavioral Measurement

Published on: November 17, 2012

19.7K
Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans
08:24

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

Published on: September 13, 2017

8.3K

Related Experiment Videos

Last Updated: Jan 16, 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

501
C. elegans Tracking and Behavioral Measurement
07:36

C. elegans Tracking and Behavioral Measurement

Published on: November 17, 2012

19.7K
Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans
08:24

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

Published on: September 13, 2017

8.3K

Area of Science:

  • Dynamical systems theory
  • Chaos theory
  • Atmospheric science modeling

Background:

  • The Lorenz-84 model exhibits weakly dissipative chaotic dynamics.
  • Classical analysis methods are insufficient for its complex structure.

Purpose of the Study:

  • To investigate the three-dimensional structure of the Lorenz-84 attractor.
  • To identify novel mechanisms driving its chaotic behavior.

Main Methods:

  • Introduction of a novel color tracer mapping technique.
  • Extraction and analysis of the attractor's 3D geometry.
  • Representation on a 2D branched manifold.
  • Validation using extracted periodic orbits.

Main Results:

  • The attractor exhibits a nontrivial toroidal chaos structure organized around a period-2 cavity.
  • A new multidirectional stretching mechanism generating chaos was identified.
  • The structure was successfully mapped onto a 2D branched manifold.

Conclusions:

  • The study reveals the intricate toroidal structure of the Lorenz-84 attractor.
  • A novel multidirectional stretching mechanism contributes to its chaotic dynamics.
  • The color tracer mapping provides effective tools for analyzing complex attractors.