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Evaluation of dynamical models: dissipative synchronization and other techniques
Luis Antonio Aguirre1, Edgar Campos Furtado, Leonardo A B Tôrres
1Laboratório de Modelagem, Análise e Controle de Sistemas Não-Lineares, Programa de Pós-Graduação em Engenharia Elétrica, Universidade Federal de Minas Gerais, Brazil. aguirre@cpdee.ufmg.br
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
A new method validates nonlinear models by checking if data and model synchronize dynamically. This approach effectively identifies key system features like bifurcations with high accuracy and low computational cost.
Area of Science:
- Nonlinear dynamics
- Model validation
- Data-driven modeling
Background:
- Validating nonlinear models from data is challenging.
- Existing methods may lack discriminating power or be computationally expensive.
Purpose of the Study:
- To review recent developments in nonlinear model validation.
- To propose and investigate a novel validation procedure based on dissipative synchronization.
Main Methods:
- The proposed method uses dissipative synchronization between data and model.
- It focuses on dynamical properties, not statistical issues.
- Tested on Duffing-Ueda, Duffing-Holmes, van der Pol oscillators, and Hénon map.
Main Results:
- The dissipative synchronization procedure effectively validates nonlinear models.
- It accurately reproduces dominant dynamical features, such as bifurcations.
- Its discriminating power is comparable to bifurcation diagrams.
Conclusions:
- The proposed validation method offers a computationally efficient alternative.
- It successfully validates models by assessing their ability to capture system dynamics.
- This approach is particularly useful for models needing to reproduce key dynamical features.
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