Abstract
We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A. J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact correctly on the lower-dimensional manifold so that the dynamics predicted by the reduced, stochastic system agrees well with the dynamics predicted by the original, high-dimensional stochastic system. The method may be applied to any system with well-separated time scales. In this article, we consider a physical problem that involves a singularly perturbed Duffing oscillator as well as a biological problem that involves the prediction of infectious disease outbreaks.
| Original language | English |
|---|---|
| Title of host publication | Interdisciplinary Mathematical Sciences |
| Publisher | World Scientific Publishing Co. Pte. Ltd. |
| Pages | 37-61 |
| Number of pages | 25 |
| DOIs | |
| State | Published - 1 Jan 2019 |
Publication series
| Name | Interdisciplinary Mathematical Sciences |
|---|---|
| Volume | 20 |
| ISSN (Print) | 1793-1355 |
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Model reduction in stochastic environments. / Forgoston, E.; Billings, L.; Schwartz, I. B.
Interdisciplinary Mathematical Sciences. World Scientific Publishing Co. Pte. Ltd., 2019. p. 37-61 (Interdisciplinary Mathematical Sciences; Vol. 20).Research output: Chapter in Book/Report/Conference proceeding › Chapter
TY - CHAP
T1 - Model reduction in stochastic environments
AU - Forgoston, E.
AU - Billings, L.
AU - Schwartz, I. B.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A. J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact correctly on the lower-dimensional manifold so that the dynamics predicted by the reduced, stochastic system agrees well with the dynamics predicted by the original, high-dimensional stochastic system. The method may be applied to any system with well-separated time scales. In this article, we consider a physical problem that involves a singularly perturbed Duffing oscillator as well as a biological problem that involves the prediction of infectious disease outbreaks.
AB - We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A. J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact correctly on the lower-dimensional manifold so that the dynamics predicted by the reduced, stochastic system agrees well with the dynamics predicted by the original, high-dimensional stochastic system. The method may be applied to any system with well-separated time scales. In this article, we consider a physical problem that involves a singularly perturbed Duffing oscillator as well as a biological problem that involves the prediction of infectious disease outbreaks.
UR - http://www.scopus.com/inward/record.url?scp=85065659584&partnerID=8YFLogxK
U2 - 10.1142/9789811200359_0003
DO - 10.1142/9789811200359_0003
M3 - Chapter
AN - SCOPUS:85065659584
T3 - Interdisciplinary Mathematical Sciences
SP - 37
EP - 61
BT - Interdisciplinary Mathematical Sciences
PB - World Scientific Publishing Co. Pte. Ltd.
ER -