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Title: Modelling a Moore-Spiegel Electronic Circuit : the imperfect model scenario
Author: Machete, R. L.
ISNI:       0000 0001 3615 2602
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2007
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The goal of this thesis is to investigate model imperfection in the context of forecasting. We focus on an electronic circuit built in a laboratory and then enclosed to reduce environmental effects. The non-dimensionalised model equations, obtained by applying Kirchhoff’s current and voltage laws, are the Moore-Spiegel Equations [47], but they exhibit a large disparity with the circuit. At parameter values used in the circuit, they yield a periodic trajectory whilst the circuit exhibits chaotic behaviour. Therefore, alternative models for the circuit are sought. The models we consider are local and global prediction models constructed from data. We acknowledge that all our models have errors and then seek to quantify how these errors are distributed across the circuit attractor. To this end, q-pling times of initial uncertainties are computed for the various models. A q-pling time is the time for an initial uncertainty to increase by a factor of q [67], where q is a real number. Whereas it is expected that different models should have different q-pling time distributions, it is found that the diversity in our models can be increased by constructing them in different coordinate spaces. To forecast the future dynamics of the circuit using any of the models, we make probabilistic forecasts [8]. The question of how to choose the spread of the initial ensemble is addressed by the use of skill scores [8, 9]. Finally, the diversity in our models is exploited by combining probabilistic forecasts from them so as to minimise some skill score. It is found that the skill of combined not-so-good models can be increased by combining them as discussed in this thesis.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Dynamical systems and ergodic theory ; Ordinary differential equations