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

Classification of Systems-I01:26

Classification of Systems-I

709
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
709
Linear time-invariant Systems01:23

Linear time-invariant Systems

1.1K
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
1.1K
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...
1.1K
Multimachine Stability01:25

Multimachine Stability

633
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
633
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

1.1K
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
1.1K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

457
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....
457

You might also read

Related Articles

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

Sort by
Same author

A synthetic cell microreactor with two types of interacting dynamic DNA-based pores.

Nature chemistry·2026
Same author

Temporal and spatial patterns of leaf unrolling in <i>Pilea peperomioides</i>.

Journal of biosciences·2026
Same author

Response to dynamic shape changes in suspensions of hard rectangles.

Soft matter·2026
Same author

Statistics and morphologies of stable droplets in scalar active fluids.

Physical review. E·2026
Same author

Beyond the bilayer: multilayered hygroscopic actuation in pine cone scales.

Beilstein journal of nanotechnology·2025
Same author

Negative Drag Force on Beating Flagellar-Shaped Bodies in Active Fluids.

Physical review letters·2025

Related Experiment Video

Updated: Apr 19, 2026

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism
08:44

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism

Published on: October 17, 2025

864

Mutual Linearity Is a Generic Property of Steady-State Markov Networks.

Robin Bebon1, Thomas Speck1

  • 1University of Stuttgart, Institute for Theoretical Physics IV, Heisenbergstr. 3, 70569 Stuttgart, Germany.

Physical Review Letters
|April 17, 2026
PubMed
Summary

We found that in complex systems, state probabilities are linearly related even under perturbation. This linearity extends to various observables, offering new insights into system dynamics.

More Related Videos

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K
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

706

Related Experiment Videos

Last Updated: Apr 19, 2026

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism
08:44

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism

Published on: October 17, 2025

864
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K
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

706

Area of Science:

  • Nonequilibrium statistical physics
  • Complex systems analysis
  • Markov network dynamics

Background:

  • Predicting complex system responses to perturbations is a key challenge.
  • Continuous-time Markov networks are used to model these systems.

Purpose of the Study:

  • To understand how continuous-time Markov networks respond to edge perturbations.
  • To explore the relationship between state probabilities and observables under steady-state conditions.

Main Methods:

  • Perturbing single edges in continuous-time Markov networks.
  • Analyzing steady-state probabilities and observables.
  • Applying the Markov chain tree theorem.

Main Results:

  • Steady-state probabilities of any two states are linearly related.
  • This linearity extends to currents, counting, and state-dependent observables.
  • An exact relation connects relative probability response to ratios of steady-state probabilities.

Conclusions:

  • System probabilities and observables are constrained by network topology and kinetics.
  • Analytical expressions for these constraints were derived using spanning tree polynomials.
  • The findings are general and applicable far from equilibrium.