Document Detail

Building dynamical models from data and prior knowledge: the case of the first period-doubling bifurcation.
MedLine Citation:
PMID:  17995094     Owner:  NLM     Status:  PubMed-not-MEDLINE    
This paper reviews some aspects of nonlinear model building from data with (gray box) and without (black box) prior knowledge. The model class is very important because it determines two aspects of the final model, namely (i) the type of nonlinearity that can be accurately approximated and (ii) the type of prior knowledge that can be taken into account. Such features are usually in conflict when it comes to choosing the model class. The problem of model structure selection is also reviewed. It is argued that such a problem is philosophically different depending on the model class and it is suggested that the choice of model class should be performed based on the type of a priori available. A procedure is proposed to build polynomial models from data on a Poincaré section and prior knowledge about the first period-doubling bifurcation, for which the normal form is also polynomial. The final models approximate dynamical data in a least-squares sense and, by design, present the first period-doubling bifurcation at a specified value of parameters. The procedure is illustrated by means of simulated examples.
Luis Antonio Aguirre; Edgar Campos Furtado
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Publication Detail:
Type:  Journal Article     Date:  2007-10-23
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  76     ISSN:  1539-3755     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2007 Oct 
Date Detail:
Created Date:  2007-11-12     Completed Date:  2008-02-29     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  046219     Citation Subset:  -    
Laboratório de Modelagem, Análise e Controle de Sistemas Não-Lineares, Programa de Pós-Graduação em Engenharia Elétrica, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31270-901 Belo Horizonte, M.G., Brazil.
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