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-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model01:14

Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model

The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A higher...
Second Order systems II01:18

Second Order systems II

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.
If  ζ...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Transient and Steady-state Response01:24

Transient and Steady-state Response

In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...

You might also read

Related Articles

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

Sort by
Same author

System-size expansion of the moments of a master equation.

Chaos (Woodbury, N.Y.)·2018
Same author

Analytical and numerical study of the non-linear noisy voter model on complex networks.

Chaos (Woodbury, N.Y.)·2018
Same author

Stochastic thermodynamics for Ising chain and symmetric exclusion process.

Physical review. E·2017
Same author

Stochastic thermodynamics for linear kinetic equations.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015
Same author

Stochastic functionals and fluctuation theorem for multikangaroo processes.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014
Same author

Fragmentation transition in a coevolving network with link-state dynamics.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014
Same journal

Correction to: 'Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes' (2020), by Mingotti et al.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

A stable hothouse triggered by a tipping mechanism.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Global stability of the Atlantic overturning circulation: edge state, long transients and boundary crisis under CO2 forcing.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Morse index classification and landscape of Kuramoto system for Hebbian-based binary pattern recognition.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Interpretable and equation-free response theory for complex systems.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
See all related articles

Related Experiment Video

Updated: May 8, 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

Stochastic description of delayed systems.

L F Lafuerza1, R Toral

  • 1IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos, CSIC-UIB, Campus UIB, 07122 Palma de Mallorca, Spain.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 21, 2013
PubMed
Summary
This summary is machine-generated.

This study analyzes stochastic birth and death processes with delays. We present analytical methods for non-Markovian systems, exploring how delays impact system fluctuations and correlations.

Keywords:
delaymaster equationsstochastic processes

More Related Videos

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
08:25

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy

Published on: April 27, 2021

Related Experiment Videos

Last Updated: May 8, 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

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
08:25

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy

Published on: April 27, 2021

Area of Science:

  • Stochastic processes
  • Mathematical biology
  • Non-Markovian systems

Background:

  • Stochastic birth and death processes are fundamental models in various scientific fields.
  • Incorporating delays into these models is crucial for accurately representing real-world systems.
  • Analyzing non-Markovian dynamics, especially with delays, presents significant analytical challenges.

Purpose of the Study:

  • To develop analytical methods for general stochastic birth and death processes with delays.
  • To investigate the impact of both constant and stochastic delays on system dynamics.
  • To understand the interplay between stochasticity and delay in influencing fluctuations and time correlations.

Main Methods:

  • Development of novel analytical approaches for non-Markovian systems.
  • Formulation of methods applicable to arbitrary probability distributions for stochastic delays.
  • Mathematical analysis of system fluctuations and time correlations under delayed conditions.

Main Results:

  • Established analytical treatments for stochastic birth and death processes with constant and stochastic delays.
  • Demonstrated the significant influence of delay on system fluctuations.
  • Quantified the effects of delay on temporal correlations within the processes.

Conclusions:

  • The developed analytical methods provide a robust framework for studying delayed stochastic systems.
  • Delay is a critical factor that modifies the stochastic behavior and temporal dependencies.
  • This work offers insights into the dynamics of complex systems where both randomness and time lags are present.