Normal form transforms separate slow and fast modes in stochastic dynamical systems

Roberts, A. J. (2008) Normal form transforms separate slow and fast modes in stochastic dynamical systems. Physica A: Statistical Mechanics and Its Applications, 387 (1). pp. 12-38. ISSN 0378-4371

Abstract

Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from insignificant detailed microscale dynamics. We explore such coordinate transforms of stochastic differential systems when the dynamics has both slow modes and quickly decaying modes. The thrust is to derive normal forms useful for macroscopic modelling of complex stochastic microscopic systems. Thus we not only must reduce the dimensionality of the dynamics, but also endeavour to separate \emph{all} slow processes from \emph{all} fast time processes, both deterministic and stochastic. Quadratic stochastic effects in the fast modes contribute to the drift of the important slow modes. Some examples demonstrate that the coordinate transform may be only locally valid or may be globally valid depending upon the dynamical system. The results will help us accurately model, interpret and simulate multiscale stochastic systems.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher.
Depositing User: Prof Tony Roberts
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 14 Dec 2007 05:14
Last Modified: 02 Jul 2013 22:53
Uncontrolled Keywords: stochastic dynamical systems; multiscale modelling
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0199 Other Mathematical Sciences > 019999 Mathematical Sciences not elsewhere classified
01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1016/j.physa.2007.08.023
URI: http://eprints.usq.edu.au/id/eprint/3496

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