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Forcing Function Diagnostics for Nonlinear Dynamics
Author(s) -
Hooker Giles
Publication year - 2009
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2008.01172.x
Subject(s) - forcing (mathematics) , nonlinear system , function (biology) , dynamics (music) , statistical physics , mathematics , computer science , physics , mathematical analysis , biology , quantum mechanics , evolutionary biology , acoustics
Summary This article investigates the problem of model diagnostics for systems described by nonlinear ordinary differential equations (ODEs). I propose modeling lack of fit as a time‐varying correction to the right‐hand side of a proposed differential equation. This correction can be described as being a set of additive forcing functions, estimated from data. Representing lack of fit in this manner allows us to graphically investigate model inadequacies and to suggest model improvements. I derive lack‐of‐fit tests based on estimated forcing functions. Model building in partially observed systems of ODEs is particularly difficult and I consider the problem of identification of forcing functions in these systems. The methods are illustrated with examples from computational neuroscience.