Multiscale couplings in prototype hybrid deterministic/stochastic systems. II: stochastic closures
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.
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