Related Experiment Video
Updated: Jan 30, 2026
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
Summary
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.
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.
Related Concept Videos
01:27Phase 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
01:24Approximate 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
01:26Linearization 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
01:24Numerical 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...
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
01:28Accuracy, 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...
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
01:29Application 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