Related Experiment Video
Updated: Jul 11, 2025

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
Published on: January 31, 2020
Forced Traveling Waves in a Reaction-Diffusion Equation with Strong Allee Effect and Shifting Habitat
1Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA.
Abstract:
We study a reaction-diffusion equation that describes the growth of a population with a strong Allee effect in a bounded habitat which shifts at a speed [Formula: see text]. We demonstrate that the existence of forced positive traveling waves depends on habitat size L, and [Formula: see text], the speed of traveling wave for the corresponding reaction-diffusion equation with the same growth function all over the entire unbounded spatial domain. It is shown that for [Formula: see text] there exists a positive number [Formula: see text] such that for [Formula: see text] there are two positive traveling waves and for [Formula: see text] there is no positive traveling wave. It is also shown if [Formula: see text] for any [Formula: see text] there is no positive traveling wave. The dynamics of the equation are further explored through numerical simulations.
Related Concept Videos
Le Chatelier's Principle: Changing Concentration
Hardy-Weinberg Principle
Genetic Drift
Mutation, Gene Flow, and Genetic Drift
Temperature Dependence on Reaction Rate
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...
Gene Flow

