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

The Integrated Rate Law: The Dependence of Concentration on Time02:39

The Integrated Rate Law: The Dependence of Concentration on Time

36.0K
While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
36.0K
Dynamic Equilibrium02:20

Dynamic Equilibrium

63.4K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
63.4K
Le Chatelier's Principle: Changing Concentration02:27

Le Chatelier's Principle: Changing Concentration

54.9K
A system at equilibrium is in a state of dynamic balance, with forward and reverse reactions taking place at equal rates. If an equilibrium system is subjected to a change in conditions that affects these reaction rates differently (a stress), then the rates are no longer equal and the system is not at equilibrium. The system will subsequently experience a net reaction in the direction of a greater rate (a shift) that will re-establish the equilibrium. This phenomenon is summarized by Le...
54.9K
Multi-Step Reactions02:31

Multi-Step Reactions

7.5K
Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
7.5K
Consecutive Reactions01:22

Consecutive Reactions

96
Consecutive reactions involve a sequence where the product of a preceding reaction becomes the reactant for the subsequent one. In a simple scheme, A transforms into B, which further reacts to form C, with rate constants k1 and k2, respectively. This concept is evident in the radioactive decay series. Assuming an initial state with only A present, the conservation of matter leads to three coupled differential equations, determining the concentrations of A, B, and C over time.The rate of change...
96
Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model01:14

Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model

147
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...
147

You might also read

Related Articles

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

Sort by
Same author

Discrete Time Crystals in Actively Mode-Locked Lasers.

Physical review letters·2026
Same author

Normal dispersion Kerr cavity solitons: beyond the mean-field limit.

Optics letters·2024
Same author

Pulse instabilities in harmonic active mode-locking: a time-delayed approach.

Optics letters·2024
Same author

Square waves and Bykov T-points in a delay algebraic model for the Kerr-Gires-Tournois interferometer.

Chaos (Woodbury, N.Y.)·2023
Same author

Stationary broken parity states in active matter models.

Physical review. E·2023
Same author

Temporal localized states and square-waves in semiconductor micro-resonators with strong time-delayed feedback.

Chaos (Woodbury, N.Y.)·2023

Related Experiment Video

Updated: May 5, 2026

Assessment of Dictyostelium discoideum Response to Acute Mechanical Stimulation
10:40

Assessment of Dictyostelium discoideum Response to Acute Mechanical Stimulation

Published on: November 9, 2017

6.4K

Dynamics of localized structures in reaction-diffusion systems induced by delayed feedback.

Svetlana V Gurevich1

  • 1Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany. gurevics@uni-muenster.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 18, 2013
PubMed
Summary

Time-delayed feedback in reaction-diffusion systems can create complex dynamics. Varying delay and feedback strength leads to pattern formation and spontaneous motion, explained by bifurcation analysis.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

7.6K
Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.0K

Related Experiment Videos

Last Updated: May 5, 2026

Assessment of Dictyostelium discoideum Response to Acute Mechanical Stimulation
10:40

Assessment of Dictyostelium discoideum Response to Acute Mechanical Stimulation

Published on: November 9, 2017

6.4K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

7.6K
Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.0K

Area of Science:

  • Chemical kinetics
  • Nonlinear dynamics
  • Mathematical modeling

Background:

  • Reaction-diffusion systems exhibit complex spatiotemporal patterns.
  • Localized structures in such systems are crucial for understanding emergent behaviors.
  • Time-delayed feedback introduces novel dynamics not present in systems without delays.

Purpose of the Study:

  • Investigate the stability properties of localized structures in a three-component reaction-diffusion system.
  • Analyze the impact of time-delayed feedback on system dynamics.
  • Characterize the complex behaviors arising from variations in delay time and feedback strength.

Main Methods:

  • Bifurcation analysis of the delayed system.
  • Derivation of an order parameter equation for localized structure position.
  • Transformation of the governing equation to a normal form for pitchfork drift bifurcation.

Main Results:

  • Variations in delay time and feedback strength induce complex dynamics.
  • Observed phenomena include target pattern formation, spontaneous motion, and spontaneous breathing.
  • The system exhibits various complex structures resulting from combined oscillatory instabilities.

Conclusions:

  • Time-delayed feedback significantly alters the stability and behavior of localized structures.
  • The study provides a detailed analysis of spontaneous motion via bifurcation theory.
  • The derived order parameter equation offers insights into the temporal evolution and control of localized structures.