Métodos de predição aplicados a sistemas dinâmicos caóticos

Abstract

Resumo: Neste estudo sao propostos metodos preditivos aplicaveis a sistemas dinamicos caoticos. Delimita-se o problema geral de predicao ao prognostico da duracao de regimes ao longo da trajetoria. Para esse fim, sao definidas regioes no espaco de estados dos sistema de Lorenz e modelo geomagnetico de Rikitake, de tal forma que os regimes se dao pelo transito entre essas regioes. Sao investigados, como variaveis preditoras, os angulos formados por pares de vetores covariantes de Lyapunov ao longo dos regimes. Tambem considera-se o uso de informacoes advindas de bred-vectors. A associacao das variaveis preditoras, em pares, elimina problemas de ambiguidade observados nas aplicacoes individuais. Essa abordagem permite elevar a taxa de acertos da predicao. Para estabelecer a relacao entre as variaveis preditoras e a duracao de regimes futuros, empregam-se ensembles de multilayer perceptrons e, independentemente, faz-se uso de um algoritmo k-NN. Obtem-se taxas de acerto de predicao de ate 99.88%.

Abstract: In this study, predictive methods applicable to chaotic dynamic systems are proposed. The general problem of prediction is delimited to the prognosis of the duration of regimes along the trajectory. For this purpose, regions in the state space of the Lorenz system and the Rikitake geomagnetic model are defined, in such a way that the regimes occur through transit between these regions. The angles formed by pairs of covariant Lyapunov vectors along the regimes are investigated as predictor variables. The use of information from bred-vectors is also considered. The association of predictor variables, in pairs, eliminates ambiguity problems observed in individual applications. This approach allows us to increase the prediction precision. To establish the relationship between the predictor variables and the duration of future regimes, ensembles of multilayer perceptrons are used and, independently, an algorithm k-NN is used. Prediction precision of up to 99.88% are achieved.