Data di Pubblicazione:
2012
Citazione:
The role of stochasticity in a model of retinal angiogenesis / V. Capasso, D. Morale, G. Facchetti. - In: IMA JOURNAL OF APPLIED MATHEMATICS. - ISSN 0272-4960. - 77:6(2012 Dec), pp. 729-747. [10.1093/imamat/hxs050]
Abstract:
The macroscopic behaviour of dissipative stochastic partial differential equations usually can be
described by a finite-dimensional system. This article proves that a macroscopic reduced model may
be constructed for stochastic reaction–diffusion equations by artificially separating the system into two
distinct slow and fast time parts. An averaging method and a deviation estimate show that the macroscopic
reduced model should be a stochastic ordinary equation that includes emergent random effects
transmitted from the microscopic scales due to the non-linear interaction. Numerical simulations of an
example stochastic reaction–diffusion equation verifies the predictions of this stochastic modelling theory.
This theory empowers us to better model the dynamics of complex stochastic systems on a large time
scale.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
angiogenesis; complex systems; hybrid models; stochastic differential equations; stochastic processes
Elenco autori:
V. Capasso, D. Morale, G. Facchetti
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