Centro Investigación en Educación Superior

First-passage times for pattern formation in nonlocal partial differential equations

CATEGORÍA(S): , , , .
AUTOR(ES): Manuel O, Caceres / Miguel Angel, Fuentes.
Licencia Creative Commons Reconocimiento CC BY. Esta obra está bajo una Licencia Creative Commons Reconocimiento CC BY 4.0 Internacional.

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-passagetime 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.

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