Multiscale couplings in prototype hybrid deterministic/stochastic systems. II: stochastic closures. (English) Zbl 1101.34042

Katsoulakis, M. A.; Majda, A. J.; Sopasakis, A.

Commun. Math. Sci. 3, No. 3, 453-478 (2005).

This paper continues the studies of the authors [Commun. Math. Sci. 2, No. 2, 255–294 (2004; Zbl 1103.93013)]. Certain couplings of stochastic models to deterministic differential equations are under investigations. The influence of noise on its overall dynamics is examined. The studied hybrid systems demonstrate that deterministic closures based on the method of separation of scales cannot capture decisive features of underlying dynamics. Therefore, a coarse grained stochastic closure is suggested. This stochastic closure describes correctly the dynamical behavior of the solutions of certain test cases.

Reviewer: Henri Schurz (Carbondale)

MSC:

34F05	Ordinary differential equations and systems with randomness
93E99	Stochastic systems and control
34E13	Multiple scale methods for ordinary differential equations

Keywords:

coupled stochastic hybrid systems; deterministic closures; stochastic closures; averaging; bifurcations; multi scale interaction; critical phenomena; differential equations; Monte Carlo methods

Citations:

Zbl 1103.93013