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

Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

2.6K
A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
2.6K
Second Order systems II01:18

Second Order systems II

483
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
483
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

432
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
432
First Order Systems01:21

First Order Systems

493
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
493
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.1K
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...
1.1K
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

709
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
709

You might also read

Related Articles

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

Sort by
Same author

Computing nonequilibrium transport from short-time transients: From Lorentz gas to heat conduction in one-dimensional chains.

The Journal of chemical physics·2026
Same author

Anomalous transport models for fluid classification: insights from an experimentally driven approach.

Discover nano·2025
Same author

Particle transport in open polygonal billiards: A scattering map.

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

Destructive effect of fluctuations on the performance of a Brownian gyrator.

Soft matter·2024
Same author

Fluctuation Relation for the Dissipative Flux: The Role of Dynamics, Correlations and Heat Baths.

Entropy (Basel, Switzerland)·2024
Same author

Probability Turns Material: The Boltzmann Equation.

Entropy (Basel, Switzerland)·2024
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Mar 29, 2026

Measuring Delay Discounting in Humans Using an Adjusting Amount Task
07:47

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

16.1K

Exact Response Theory for Delay Equations.

Federico Gollinucci1,2, Enrico Ortu1,2,3, Lamberto Rondoni1,2

  • 1Department of Mathematical Sciences "Giuseppe Luigi Lagrange", Politecnico di Torino, 10129 Torino, Italy.

Entropy (Basel, Switzerland)
|March 28, 2026
PubMed
Summary
This summary is machine-generated.

Exact response theory, or Transient Time Correlation Function formalism, is extended to time-lagged systems. This method maps delay dynamics into an augmented phase space for calculating exact system responses.

Keywords:
Transient Time Correlation Functiondissipation functionuncertainty quantification

More Related Videos

Measurement & Analysis of the Temporal Discrimination Threshold Applied to Cervical Dystonia
10:05

Measurement & Analysis of the Temporal Discrimination Threshold Applied to Cervical Dystonia

Published on: January 27, 2018

10.3K
Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
08:13

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

6.9K

Related Experiment Videos

Last Updated: Mar 29, 2026

Measuring Delay Discounting in Humans Using an Adjusting Amount Task
07:47

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

16.1K
Measurement & Analysis of the Temporal Discrimination Threshold Applied to Cervical Dystonia
10:05

Measurement & Analysis of the Temporal Discrimination Threshold Applied to Cervical Dystonia

Published on: January 27, 2018

10.3K
Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
08:13

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

6.9K

Area of Science:

  • Theoretical Physics
  • Chemical Physics
  • Dynamical Systems Theory

Background:

  • Exact response theory (Transient Time Correlation Function formalism) analyzes system dynamics perturbations.
  • Linear response theory is limited to small perturbations.
  • Generic dynamical systems require advanced response formalisms.

Purpose of the Study:

  • Adapt exact response theory for time-lagged systems.
  • Illustrate the adapted theory with delay equations.
  • Compare linear and exact response approaches.

Main Methods:

  • Extension of exact response theory to incorporate time-lagged dynamics.
  • Mapping delay-dependent dynamics into a higher-dimensional, autonomous augmented phase space.
  • Utilizing techniques for time-dependent perturbations in deterministic and stochastic systems.

Main Results:

  • The adapted theory provides a framework for computing exact responses in time-lagged systems.
  • Demonstrated applicability using simple delay equations with memory terms.
  • Established the autonomy of the dynamics in the augmented phase space.

Conclusions:

  • Exact response theory is successfully extended to handle time-lagged systems.
  • The augmented phase space approach simplifies computation of exact responses.
  • Further investigation into linear versus exact approaches is warranted.