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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
Quadratic Models01:23

Quadratic Models

Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...

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

Structure analysis of the Lorenz-84 chaotic attractor.

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

Earthworm activity and its coupling to soil hydrology: A deterministic analysis.

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

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

Epidemiology and infection·2020
Same author

The role of predation risk in metamorphosis versus behavioural avoidance: a sex-specific study in a facultative paedomorphic amphibian.

Oecologia·2019
Same author

Linkages between common wheat yields and climate in Morocco (1982-2008).

International journal of biometeorology·2013

Related Experiment Video

Updated: May 16, 2026

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy
11:53

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Published on: October 14, 2017

Polynomial search and global modeling: Two algorithms for modeling chaos.

S Mangiarotti1, R Coudret, L Drapeau

  • 1Centre d'Études Spatiales de la Biosphère, UPS-CNRS- CNES-IRD, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary

Global modeling uses polynomial ordinary differential equations to describe dynamical systems. Algorithms like Polynomial Model Search (PoMoS) and Global Modeling (GloMo) identify model structures and parameters from time series data.

More Related Videos

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

Related Experiment Videos

Last Updated: May 16, 2026

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy
11:53

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Published on: October 14, 2017

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

Area of Science:

  • Dynamical Systems Analysis
  • Computational Modeling
  • Scientific Computing

Background:

  • Global modeling seeks concise mathematical representations of observed dynamical systems.
  • Existing algorithms like Polynomial Model Search (PoMoS) and Global Modeling (GloMo) utilize polynomial ordinary differential equations.
  • These algorithms are designed to work with limited time series data.

Purpose of the Study:

  • To describe the PoMoS and GloMo algorithms for global modeling from single time series.
  • To demonstrate the application of these algorithms through diverse examples.
  • To enhance the understanding and application of polynomial-based dynamical system modeling.

Main Methods:

  • Utilizing the Global Modeling (GloMo) algorithm for parameter identification and structure selection from single time series.
  • Employing Polynomial Model Search (PoMoS) for identifying polynomial formulations from time series.
  • Applying visualization tools such as first return maps and Lyapunov exponent computation for dynamical system characterization.

Main Results:

  • Successfully applied global modeling to the Rössler attractor, showcasing its ability to model chaotic systems.
  • Obtained a less parsimonious global model for copper electrodissolution in phosphoric acid, validating its application in experimental analysis.
  • Explored the application of global modeling to agricultural systems, using vegetation index data for semiarid wheat cycles.

Conclusions:

  • The PoMoS and GloMo algorithms provide a robust framework for global modeling of dynamical systems from time series.
  • The demonstrated examples highlight the versatility of the algorithms across chaotic attractors, experimental chemical systems, and agricultural processes.
  • Further application of these polynomial-based modeling techniques can lead to more concise and insightful descriptions of complex phenomena.