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

Modeling with Differential Equations01:25

Modeling with Differential Equations

83
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...
83
Equation of Rotational Dynamics01:08

Equation of Rotational Dynamics

14.8K
Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...
14.8K
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1000
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
1000
Separable Differential Equations01:20

Separable Differential Equations

90
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
90
Introduction to Differential Equations01:20

Introduction to Differential Equations

125
A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
125
Linear Differential Equations01:27

Linear Differential Equations

82
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
82

You might also read

Related Articles

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

Sort by
Same author

Interfacial Self-Healing Polymer Electrolytes With Gradient Covalent-Noncovalent Dynamic Bonds for 4.6 V-Class Lithium Metal Batteries.

Advanced materials (Deerfield Beach, Fla.)·2026
Same author

Shared and Unique Patterns of Dysregulated Dual Systems Between Adolescent Problematic Video Gaming and ADHD.

PsyCh journal·2026
Same author

Regenerative Artificial Solid Electrolyte Interphase via Dynamic Cross-Linking for Stable Lithium Metal Anodes.

Angewandte Chemie (International ed. in English)·2026
Same author

Revealing competitive interfacial reactions in high-energy Li-S batteries.

Nature·2026
Same author

Ultrafast Joule-Heating Disproportionation for Engineering Sub-2 nm Si Nanodomains toward Stable, High-Performance SiO Anodes.

Journal of the American Chemical Society·2026
Same author

Interstitial-Hydrogen-Modulated Subnanometer PdPtIrCoNiH High-Entropy Hydride Nanowires for Efficient Hydrogen Electrocatalysis.

Journal of the American Chemical Society·2026

Related Experiment Video

Updated: Feb 2, 2026

Modeling Verbal Behavior Deficits with the Stimulus Control Ratio Equation, SCoRE
06:57

Modeling Verbal Behavior Deficits with the Stimulus Control Ratio Equation, SCoRE

Published on: May 14, 2019

10.9K

Dynamic Regulation Responding to an External Stimulus: A Differential Equation Model.

Yueqin Hu1, Yunhui Huang2

  • 1a Department of Psychology , Texas State University.

Multivariate Behavioral Research
|November 21, 2018
PubMed
Summary

This study introduces a driven damped oscillator model to better describe dynamic regulation processes with non-zero steady states. The new model accurately estimates parameters, improving upon traditional models for external stimulus responses.

Keywords:
Differential equation modelsdynamical systemsexternal stimulusregulationsteady state

More Related Videos

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

4.1K
Progressive-ratio Responding for Palatable High-fat and High-sugar Food in Mice
11:16

Progressive-ratio Responding for Palatable High-fat and High-sugar Food in Mice

Published on: May 3, 2012

22.8K

Related Experiment Videos

Last Updated: Feb 2, 2026

Modeling Verbal Behavior Deficits with the Stimulus Control Ratio Equation, SCoRE
06:57

Modeling Verbal Behavior Deficits with the Stimulus Control Ratio Equation, SCoRE

Published on: May 14, 2019

10.9K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

4.1K
Progressive-ratio Responding for Palatable High-fat and High-sugar Food in Mice
11:16

Progressive-ratio Responding for Palatable High-fat and High-sugar Food in Mice

Published on: May 3, 2012

22.8K

Area of Science:

  • Dynamic systems analysis
  • Mathematical modeling
  • Statistical inference

Background:

  • Traditional damped oscillator models fail to capture non-zero steady states in dynamic regulation.
  • Oscillatory processes often exhibit persistent states rather than damping to zero.
  • External stimuli can induce complex dynamic responses beyond simple damping.

Purpose of the Study:

  • Introduce the driven damped oscillator model to account for non-zero steady states.
  • Develop and validate methods for estimating parameters of the new model.
  • Demonstrate the model's utility with real-world sales promotion data.

Main Methods:

  • Generalized local linear approximation for parameter estimation.
  • Continuous time structural equation modeling.
  • Analytic solutions of differential equations for model fitting.

Main Results:

  • Simulation studies confirm reliable recovery of model parameters.
  • The driven damped oscillator model effectively captures non-zero steady states.
  • Successful application to sales data following a promotion.

Conclusions:

  • The driven damped oscillator model offers a more realistic framework for dynamic regulation.
  • The proposed estimation methods are robust and effective.
  • The model has broad applicability in various scientific and business domains.