Artículo
First-passage times for pattern formation in nonlocal partial differential equations
Fecha de publicación:
10/2015
Editorial:
American Physical Society
Revista:
Physical Review E: Statistical, Nonlinear and Soft Matter Physics
ISSN:
1539-3755
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.
Palabras clave:
Stochastic Process
,
Non Local Interaction
,
Population Model
,
Mfpt
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Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Caceres Garcia Faure, Manuel Osvaldo; Fuentes, Miguel Angel; First-passage times for pattern formation in nonlocal partial differential equations; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 92; 4; 10-2015; 1-14
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