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

Cyclic Processes And Isolated Systems01:19

Cyclic Processes And Isolated Systems

3.0K
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state. 
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...
3.0K
Stability of structures01:14

Stability of structures

269
In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
269
Stability01:28

Stability

204
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...
204
Forced Oscillations01:06

Forced Oscillations

6.9K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
6.9K
Types of Damping01:20

Types of Damping

6.8K
If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
6.8K
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

5.8K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
5.8K

You might also read

Related Articles

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

Sort by
Same journal

Stochastic Poincaré maps for a slow-fast system with white noises: Approximation and visualization.

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

On a stable torus in a 3D system with a saddle-focus.

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

Targeted interventions suppress epidemic outbreaks in spatial higher-order activity-driven networks.

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

Erratum: "Hierarchical organization of bursty trains in event sequences" [Chaos 35, 113115 (2025)].

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

Deterministic control of CW/CCW alternation by dual-frequency injection in a heterogeneous oscillator ring.

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

A CTRW-driven subdiffusive fractional Brownian bridge in the reconstruction of missing experimental data.

Chaos (Woodbury, N.Y.)·2026

Related Experiment Video

Updated: Oct 8, 2025

Mechanical Stimulation of Stem Cells Using Cyclic Uniaxial Strain
25:12

Mechanical Stimulation of Stem Cells Using Cyclic Uniaxial Strain

Published on: July 29, 2007

12.9K

Stabilization of cyclic processes by slowly varying forcing.

J Newman1, M Lucas2, A Stefanovska3

  • 1Centre for Systems, Dynamics and Control, Department of Mathematics, University of Exeter, Exeter EX4 4QF, United Kingdom.

Chaos (Woodbury, N.Y.)
|January 1, 2022
PubMed
Summary

We developed a new mathematical framework for analyzing dynamical stability in finite-time processes. This approach addresses limitations of classical methods, enabling analysis of phenomena like phase stabilization.

More Related Videos

Force-Clamp Rheometry for Characterizing Protein-based Hydrogels
09:55

Force-Clamp Rheometry for Characterizing Protein-based Hydrogels

Published on: August 21, 2018

7.1K
Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
08:05

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

2.5K

Related Experiment Videos

Last Updated: Oct 8, 2025

Mechanical Stimulation of Stem Cells Using Cyclic Uniaxial Strain
25:12

Mechanical Stimulation of Stem Cells Using Cyclic Uniaxial Strain

Published on: July 29, 2007

12.9K
Force-Clamp Rheometry for Characterizing Protein-based Hydrogels
09:55

Force-Clamp Rheometry for Characterizing Protein-based Hydrogels

Published on: August 21, 2018

7.1K
Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
08:05

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

2.5K

Area of Science:

  • Mathematical Physics
  • Dynamical Systems Theory

Background:

  • Classical stability analysis often assumes infinite time scales, which is unsuitable for finite-time processes.
  • External influences on a slow timescale can complicate stability analysis in dynamical systems.
  • Existing frameworks are inadequate for certain phenomena like phase stabilization.

Purpose of the Study:

  • Introduce a novel mathematical framework for qualitative analysis of dynamical stability.
  • Adapt stability analysis for finite-time processes influenced by slow external factors.
  • Generalize and formalize the phase-stabilization phenomenon.

Main Methods:

  • Employ a slow-fast formalism for finite-time dynamical systems.
  • Define stability in the singular limit within a bounded interval for slow time.
  • Extend classical Lyapunov stability concepts to finite-time dynamics.

Main Results:

  • Developed new stability definitions analogous to classical infinite-time definitions.
  • Mathematically formalized and generalized phase-stabilization.
  • Demonstrated the framework's necessity where classical definitions fail.

Conclusions:

  • The new framework provides a robust method for analyzing dynamical stability in finite-time systems.
  • This approach is essential for understanding phenomena like phase stabilization under slow external influences.
  • Offers a generalized perspective on stability beyond traditional infinite-time assumptions.