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

Phase I Reactions: Reductive Reactions01:27

Phase I Reactions: Reductive Reactions

590
Phase I biotransformation reductive reactions are chemical processes that modify drugs by introducing or revealing polar functional groups via reduction. Enzymes called reductases catalyze these reactions, playing a pivotal role in drug metabolism by transforming lipophilic drugs into more polar, water-soluble metabolites for easy excretion. An essential type of reductive reaction is the carbonyl group reduction, where aldehydes and ketones are reduced to alcohols. An example is the...
590
Approximate Integration01:24

Approximate Integration

47
In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
47
Linearization and Approximation01:26

Linearization and Approximation

59
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
59
Numerical Calculations01:24

Numerical Calculations

1.2K
In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
1.2K
Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

1.3K
Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
1.3K
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

89
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
89

You might also read

Related Articles

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

Sort by
Same author

Optimizing charge-balanced pulse stimulation for desynchronization.

Chaos (Woodbury, N.Y.)·2022
Same author

Mutual singularities of overlapping attractor and repeller.

Chaos (Woodbury, N.Y.)·2021
Same author

Some elements for a history of the dynamical systems theory.

Chaos (Woodbury, N.Y.)·2021
Same author

Controlling collective synchrony in oscillatory ensembles by precisely timed pulses.

Chaos (Woodbury, N.Y.)·2020
Same author

Kantorovich-Rubinstein-Wasserstein distance between overlapping attractor and repeller.

Chaos (Woodbury, N.Y.)·2020
Same author

Solitary phase waves in a chain of autonomous oscillators.

Chaos (Woodbury, N.Y.)·2020
Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

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

Exact computation of Lyapunov exponents via system parameters in multi-triangle chaotic maps: Bifurcation analysis and circuit realization.

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

Integrating score-based generative modeling and neural ODEs for accurate representation of multiscale chaotic dynamics.

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

A data-driven tuberculosis model with behavioral changes and saturated treatment: Optimal control and cost-effectiveness study.

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

Breathers, rational solutions, and their exact physical spectra in F = 1 spinor Bose-Einstein condensates.

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

Finite invariant sets with bridging points in logistic IFS.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Jan 30, 2026

Quantitative Proteomics Using Reductive Dimethylation for Stable Isotope Labeling
11:53

Quantitative Proteomics Using Reductive Dimethylation for Stable Isotope Labeling

Published on: July 1, 2014

16.8K

Numerical phase reduction beyond the first order approximation.

Michael Rosenblum1, Arkady Pikovsky1

  • 1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.

Chaos (Woodbury, N.Y.)
|February 3, 2019
PubMed
Summary
This summary is machine-generated.

We present a numerical method to reconstruct phase dynamics in coupled oscillators. This approach accurately describes system behavior even with strong coupling and significant deviations from the limit cycle.

More Related Videos

Determination of the Gas-phase Acidities of Oligopeptides
11:00

Determination of the Gas-phase Acidities of Oligopeptides

Published on: June 24, 2013

11.6K
Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

10.4K

Related Experiment Videos

Last Updated: Jan 30, 2026

Quantitative Proteomics Using Reductive Dimethylation for Stable Isotope Labeling
11:53

Quantitative Proteomics Using Reductive Dimethylation for Stable Isotope Labeling

Published on: July 1, 2014

16.8K
Determination of the Gas-phase Acidities of Oligopeptides
11:00

Determination of the Gas-phase Acidities of Oligopeptides

Published on: June 24, 2013

11.6K
Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

10.4K

Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Oscillatory systems

Background:

  • Self-sustained oscillators are fundamental in various scientific fields.
  • Understanding their coupled or driven dynamics is crucial.
  • Existing models may not capture behavior under strong coupling or large deviations.

Purpose of the Study:

  • To develop a numerical approach for reconstructing phase dynamics.
  • To investigate the validity of phase-only descriptions for oscillators.
  • To analyze the nature of coupling functions in such systems.

Main Methods:

  • A simple algorithm for computing the phase of perturbed systems.
  • Numerical construction of the phase evolution equation.
  • Simulations to test the approach under varying conditions.

Main Results:

  • The phase-only description is valid for strong coupling strengths.
  • The approach remains accurate for large deviations from the limit cycle.
  • Coupling functions are critically dependent on coupling and generally non-decomposable.

Conclusions:

  • A robust numerical method for phase dynamics reconstruction is established.
  • Phase-only descriptions offer wider applicability than previously thought.
  • The study highlights the complexity of coupling functions in oscillator networks.