info:eu-repo/semantics/article
Fisher equation for anisotropic diffusion: Simulating South American human dispersals
Fecha
2007-09Registro en:
Martino, Luis Angel; Osella, Ana Maria; Dorso, Claudio Oscar; Lanata, Jose Luis; Fisher equation for anisotropic diffusion: Simulating South American human dispersals; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 76; 3; 9-2007; 1-10
1539-3755
CONICET Digital
CONICET
Autor
Martino, Luis Angel
Osella, Ana Maria
Dorso, Claudio Oscar
Lanata, Jose Luis
Resumen
The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.