Noise-induced pattern formation - Noise-induced Phenomena in the Environmental Sciences - page 182

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Figure 5.7. Weighting factors for the discretization of the Laplacian operator ∇ φ in

the cell { i , j } .

Infinitely extended random fields are generally suitably simulated by periodic
boundary conditions. Numerical simulation of the stochastic equations is not triv-
ial, and attention has to be paid to the interplay between the temporal and the spatial
discretizations and the simulation of the noise component. In this chapter we adopt
the methods described by Carrillo et al. ( 2003 )and Garcia-Ojalvo and Sancho ( 1999 ).
We refer the readers to these publications for further details.

5.1.3 Other noise-induced phenomena in spatiotemporal systems
Formation of spatial patterns is not the only noise-induced phenomenon that might be
of interest in the environmental sciences. Indeed, even though there exists no univocal
definition of noise-induced phenomena in a spatiotemporal dynamical system, a broad
definition could encompass all phenomena in which the presence of (noisy) stochastic

∇

4

φ

Figure 5.8. Weighting factors for the discretization of the biharmonic operator

in the cell { i , j } .