AI Article Synopsis
- The study examines how populations change in a circular pattern using a nonlinear reaction-diffusion model, which shows how population density evolves over time.
- The analytical solution reveals that population density spreads out over time in a wave-like motion, but curvature affects this spread if distances are not long enough.
- The results from the analytical solution match closely with the numerical simulations, confirming their accuracy.
Article Abstract
Population dynamics that evolve in a radial symmetric geometry are 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 is found. It shows that the population density evolves from the initial state and propagates in a traveling-wave-like manner for a long-time scale. If the distance is insufficiently long, the curvature has an ineluctable influence on the density profile and front speed. In comparison, the analytical solution is in agreement with the numerical solution.
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| http://dx.doi.org/10.1103/PhysRevE.89.012122 | DOI Listing |
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