Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

Restarting Stalled Replication Forks

Restarting Stalled Replication Forks

DNA replication is initiated at sites containing predefined DNA sequences known as origins of replication. DNA is unwound at these sites by the minichromosome maintenance (MCM) helicase and other factors such as Cdc45 and the associated GINS complex.The unwound single strands are protected by replication protein A (RPA) until DNA polymerase starts synthesizing DNA at the 5’ end of the strand in the same direction as the replication fork. To prevent the replication fork from falling apart, a...

Restarting Stalled Replication Forks

Restarting Stalled Replication Forks

DNA replication is initiated at sites containing predefined DNA sequences known as origins of replication. DNA is unwound at these sites by the minichromosome maintenance (MCM) helicase and other factors such as Cdc45 and the associated GINS complex.The unwound single strands are protected by replication protein A (RPA) until DNA polymerase starts synthesizing DNA at the 5’ end of the strand in the same direction as the replication fork. To prevent the replication fork from falling apart, a...

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...

Stability of structures

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...

Stability of Equilibrium Configuration

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...

You might also read

Related Articles

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

Sort by

Same author

Dispersal-induced growth or decay in a time-periodic environment. The case of reducible migration matrices.

Journal of mathematical biology·2025

Same author

The Inheritance of Local Bifurcations in Mass Action Networks.

Journal of nonlinear science·2025

Same author

Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity.

Nonlinear dynamics·2024

Same author

Oscillations in three-reaction quadratic mass-action systems.

Studies in applied mathematics (Cambridge, Mass.)·2024

Same author

Oscillations in Planar Deficiency-One Mass-Action Systems.

Journal of dynamics and differential equations·2024

Same author

When can a population spreading across sink habitats persist?

Journal of mathematical biology·2024

Search research articles

Related Experiment Video

Updated: May 19, 2026

The Replica Set Method: A High-throughput Approach to Quantitatively Measure Caenorhabditis elegans Lifespan

The Replica Set Method: A High-throughput Approach to Quantitatively Measure Caenorhabditis elegans Lifespan

Published on: June 29, 2018

Robust permanence and impermanence for stochastic replicator dynamics.

Michel Benaïm¹, Josef Hofbauer, William H Sandholm

¹Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand, Neuchâtel, Switzerland.

Journal of Biological Dynamics

|August 14, 2012

Summary

This summary is machine-generated.

Stochastic replicator dynamics show that permanence is robust against small noise. However, impermanence leads to convergence towards the state space boundary, regardless of noise intensity.

Related Experiment Videos

Last Updated: May 19, 2026

The Replica Set Method: A High-throughput Approach to Quantitatively Measure Caenorhabditis elegans Lifespan

The Replica Set Method: A High-throughput Approach to Quantitatively Measure Caenorhabditis elegans Lifespan

Published on: June 29, 2018

Area of Science:

Evolutionary Game Theory
Dynamical Systems
Stochastic Analysis

Background:

The deterministic replicator dynamics model describes evolutionary game theory.
Previous work established conditions for permanence and impermanence in deterministic models.
Stochastic perturbations introduce randomness into these dynamics.

Purpose of the Study:

To analyze the robustness of permanence and impermanence conditions under stochastic perturbations.
To investigate the behavior of stochastic replicator dynamics near attractors and boundaries.

Main Methods:

Introduced Brownian perturbations to the deterministic replicator dynamics.
Analyzed the resulting stochastic differential equations.
Examined ergodic distributions and convergence rates.

Main Results:

When deterministic dynamics are permanent, small noise leads to a unique ergodic distribution near the maximal interior attractor, indicating robust permanence.
When deterministic dynamics are impermanent, stochastic dynamics converge exponentially to the state space boundary for both small and large noise levels.

Conclusions:

Permanence in replicator dynamics is robust to small stochastic perturbations.
Impermanence in replicator dynamics leads to predictable convergence to boundary states under stochasticity.