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

Travelling Waves

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...

Propagation of Waves

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...

Propagation Speed of Electromagnetic Waves

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:

Rationalizing Substitutions

Rationalizing Substitutions

Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...

Traveling Waves: Lossless Lines

Traveling Waves: Lossless Lines

The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.

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...

You might also read

Related Articles

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

Sort by

Same author

SBRT embedded in low-dose RT plus αPD-1 (immuno-EclipseRT, iERT) elicits CD8<sup>+</sup> T cell immunity against bulky tumors via an IFN-I/NK/DC axis.

Nature communications·2026

Same author

Sex-specific patterns of skeletal muscle aging at the L3 level: a quantitative study based on opportunistic CT.

BMC musculoskeletal disorders·2026

Same author

A two-species competition model on a compact metric graph for the invasion and competition of Aedes Aegypti and Aedes Albopictus mosquitoes in Florida.

Journal of mathematical biology·2026

Same author

Optimal Neoadjuvant Approach for Resectable Esophageal Cancer in the Era of Immunotherapy.

International journal of cancer·2026

Same author

Propagation dynamics of reaction-diffusion systems in sugar beet agro-ecosystems.

Journal of mathematical biology·2026

Same author

Effect of human albumin infusion on inflammation, oxidative stress, and prognosis in decompensated cirrhosis: a prospective cohort study with a meta-analysis.

BMC gastroenterology·2026

Search research articles

Related Experiment Video

Updated: Jun 15, 2026

New Variations for Strategy Set-shifting in the Rat

New Variations for Strategy Set-shifting in the Rat

Published on: January 23, 2017

Spreading speeds and traveling waves in competitive recursion systems.

Guo Lin¹, Wan-Tong Li, Shigui Ruan

¹School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People's Republic of China. ling@lzu.edu.cn

Journal of Mathematical Biology

|February 27, 2010

Summary

This study examines traveling wave solutions in discrete time recursion systems. Interspecific competition slows the spreading speed of one species and reduces population densities.

More Related Videos

Rapid PCR Thermocycling using Microscale Thermal Convection

Rapid PCR Thermocycling using Microscale Thermal Convection

Published on: March 5, 2011

Related Experiment Videos

Last Updated: Jun 15, 2026

New Variations for Strategy Set-shifting in the Rat

New Variations for Strategy Set-shifting in the Rat

Published on: January 23, 2017

Rapid PCR Thermocycling using Microscale Thermal Convection

Rapid PCR Thermocycling using Microscale Thermal Convection

Published on: March 5, 2011

Area of Science:

Ecology
Mathematical Biology
Population Dynamics

Background:

Discrete time recursion systems model spatial spread.
Two competitive species interactions are analyzed.
Traveling wave solutions represent invasion dynamics.

Purpose of the Study:

Establish existence of traveling wave solutions.
Determine the threshold wave speed.
Analyze the impact of interspecific competition on spreading speeds and population densities.

Main Methods:

Analysis of discrete time recursion systems.
Establishing existence conditions for traveling wave solutions.
Comparing spreading speeds with and without interspecific competition.

Main Results:

Traveling wave solutions exist above a specific threshold speed.
This threshold speed equals the spreading speed of one species.
Interspecific competition significantly slows the spread of one species.
Coexisting population densities are lower with competition.

Conclusions:

Interspecific competition alters invasion dynamics.
The spreading speed threshold is species-specific.
Competition leads to reduced population densities in the coexistence domain.