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

Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

734
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
734
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

917
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
917
Pole and System Stability01:24

Pole and System Stability

828
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
828
Linear time-invariant Systems01:23

Linear time-invariant Systems

813
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...
813
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

849
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
849
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.1K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.1K

You might also read

Related Articles

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

Sort by
Same author

Effect of time-dependent forcing on pole reversals in a conceptual dynamo model.

Scientific reports·2026
Same author

Introduction to the Focus Issue: Nonautonomous dynamics in the climate sciences.

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

Magnetic structures in the explicitly time-dependent nontwist map.

Chaos (Woodbury, N.Y.)·2024
Same author

Macroscopic transport in mixed phase space Hamiltonian systems and the role of a distinct time-scale for the power-law decay.

Chaos (Woodbury, N.Y.)·2024
Same author

Characterizing chaos in systems subjected to parameter drift.

Physical review. E·2022
Same author

Chaos in conservative discrete-time systems subjected to parameter drift.

Chaos (Woodbury, N.Y.)·2021

Related Experiment Video

Updated: Dec 31, 2025

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

438

Chaos in Hamiltonian systems subjected to parameter drift.

Dániel Jánosi1, Tamás Tél1

  • 1Institute for Theoretical Physics, Eötvös Loránd University, Pázmány Péter Sétány 1/A, H-1117 Budapest, Hungary.

Chaos (Woodbury, N.Y.)
|January 3, 2020
PubMed
Summary

Parameter drifts in Hamiltonian systems create snapshot tori. Torus breakup, caused by hyperbolic orbits and chaotic seas, leads to exponential divergence, analogous to fluid vortices.

Area of Science:

  • Nonlinear dynamics
  • Hamiltonian systems
  • Chaos theory

Background:

  • Low-dimensional Hamiltonian systems are fundamental models.
  • Parameter drifts introduce time-dependence and complexity.
  • Understanding long-term dynamics under perturbations is crucial.

Purpose of the Study:

  • To analyze the dynamics of Hamiltonian systems under parameter drifts.
  • To identify the mechanisms and conditions for torus breakup.
  • To explore the relationship between intact tori and fluid vortices.

Main Methods:

  • Following ensembles of initial conditions on tori.
  • Analyzing 'snapshot tori' and their evolution.
  • Investigating collisions with hyperbolic orbits and chaotic seas.

More Related Videos

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
07:15

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

891
Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms
10:32

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms

Published on: August 15, 2016

15.9K

Related Experiment Videos

Last Updated: Dec 31, 2025

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

438
Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
07:15

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

891
Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms
10:32

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms

Published on: August 15, 2016

15.9K
  • Calculating finite-time Lyapunov exponents and using the polar rotation angle method.

    • Main Results:

    • Snapshot tori emerge, exhibiting time-dependent shapes and central elliptic orbits.
    • Torus breakup occurs due to collisions with hyperbolic orbits and chaotic seas.
    • Intact tori persist, analogous to coherent vortices in fluid dynamics.
    • Exponential divergence of initially close points signals torus breakup, characterized by a novel Lyapunov exponent.

    Conclusions:

    • Parameter drifts lead to complex dynamics and torus breakup in Hamiltonian systems.
    • Torus breakup is a critical transition driven by chaotic interactions.
    • Intact tori serve as analogs for coherent structures in fluid dynamics.
    • The study provides insights into the behavior of perturbed dynamical systems.