Radial propagation in population dynamics with density-dependent diffusion

TL;DR

This paper investigates radial population dynamics using a density-dependent reaction-diffusion model, deriving an approximate analytical solution that describes traveling wave propagation influenced by curvature effects, validated against numerical results.

Contribution

It provides an approximate analytical solution for radial population diffusion with density dependence, highlighting curvature effects on wave propagation.

Findings

Population density propagates as a traveling wave over time.

Curvature significantly influences density profiles and front speeds.

Analytical solutions agree with numerical simulations.

Abstract

The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate analytical solution to this equation has been found. It shows that the population density evolves from initial state and propagates as the traveling wave-like for the large time scale. One can be mentioned that, if the distance is insufficient large, the curvature has ineluctable influence on density profile and front speed. In comparison, the analytical solution is in agreement with the numerical solution.