Wavespeed in reaction-diffusion systems, with applications to chemotaxis and population pressure

Area of Science:

• Dynamical Systems Theory
• Mathematical Biology
• Reaction-Diffusion Systems

Background:

• Reaction-diffusion systems are fundamental in modeling biological processes.
• Understanding traveling wave dynamics is crucial for predicting pattern formation and spread.
• Perturbations can significantly alter wave behavior, necessitating robust analytical tools.

Purpose of the Study:

• To develop a theoretical framework for calculating wavespeeds in perturbed reaction-diffusion systems.
• To provide explicit formulas for wavespeed under various perturbation types.
• To propose experimental methods for distinguishing between biological mechanisms influencing wave propagation.

Main Methods:

• Application of the Melnikov function from dynamical systems theory.
• Analysis of reaction-diffusion systems with weak perturbations.
• Perturbations considered include reaction kinetics, diffusion coefficients, and active advection.

Main Results:

• Explicit formulas for wavespeed derived.
• Demonstration of how chemotaxis leads to nonlinear advection.
• Illustration of how population pressure causes density-dependent diffusion and nonlinear advection.

Conclusions:

• The Melnikov function provides an effective tool for analyzing wavespeed in perturbed reaction-diffusion systems.
• Theoretical predictions offer a basis for experimental validation.
• Distinguishing between chemotaxis and population pressure in biological systems is feasible through tailored experiments.