Simple reaction-diffusion population model on scale-free networks

TL;DR

This paper investigates a reaction-diffusion population model on scale-free networks, revealing how network topology and diffusion modifications influence critical population thresholds and species survival, supported by theoretical and simulation results.

Contribution

It introduces a mean-field framework to analyze the impact of network heterogeneity and diffusion modifications on population dynamics on scale-free networks.

Findings

Heterogeneous connectivity lowers steady population density.

Modified diffusion increases critical death rate and steady population density.

Results confirmed by computer simulations.

Abstract

We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the critical death rate, whereas the heterogeneous connectivity can cause smaller steady population density and critical population density. In the case of modified diffusion, we obtain a larger critical death rate and steady population density, at the meanwhile, lower critical population density, which is good for the survival of species. The results were obtained using a mean-field-like framework and were confirmed by computer simulations.