Quantifying chaos from time-series data through Lyapunov exponents: a computational data science approach
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2021
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05/11/2020
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Giannerini, Simone
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Universidad Complutense de Madrid
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Abstract
La aparición de la teoría del caos ha supuesto un cambio de paradigma en la ciencia. Los sistemas caóticos son sistemas dinámicos deterministas no lineales que pueden comportarse como un movimiento aparentemente errático e irregular. Tengan en cuenta que sí pudiésemos caracterizar un sistema caótico en algún sentido nos permitiría evidenciar que detrás de los mismos existe un sistema generador determinista a pesar de mostrar un comportamiento aparentemente aleatorio. Este hecho nos permitiría aprovechar ese carácter determinista para poder hacer predicciones y controlar las variables de estos sistemas dinámicos deterministas (caóticos). Los métodos y técnicas que persiguen contrastar la hipótesis del caos tratan de estimar los llamados exponentes de Lyapunov como una forma de caracterizar un sistema caótico. Hoy en día, cuantificar el caos a partir de datos de series temporales mediante este tipo de medidas cuantitativas de manera rigurosa está lejos de ser un ejercicio trivial y plantea una serie de retos teóricos y prácticos...
Chaos theory has been hailed as a revolution of thoughts and attracting ever increasing attention of many scientists from diverse disciplines. Chaotic systems are nonlinear deterministic dynamic systems which can behave like an apparently erratic and irregular motion. Keep in mind that if we could characterise a chaotic system in some sense it would allow us to evidence that a deterministic generating system exists behind that chaotic system in spite of showing an apparently random behaviour. This fact would provide us to take advantage of this deterministic character to be able to make predictions and control over the variables of these (chaotic) deterministic dynamic systems. Methods and techniques related to test the hypothesis of chaos try to estimate the so-called Lyapunov exponents as a way of characterising achaotic system. Nowadays quantifying chaos from time-series data through this kind of quantitative measure in a rigorous fashion is far from being a trivial exercise and poses a number of theoretical and practical challenges...
Chaos theory has been hailed as a revolution of thoughts and attracting ever increasing attention of many scientists from diverse disciplines. Chaotic systems are nonlinear deterministic dynamic systems which can behave like an apparently erratic and irregular motion. Keep in mind that if we could characterise a chaotic system in some sense it would allow us to evidence that a deterministic generating system exists behind that chaotic system in spite of showing an apparently random behaviour. This fact would provide us to take advantage of this deterministic character to be able to make predictions and control over the variables of these (chaotic) deterministic dynamic systems. Methods and techniques related to test the hypothesis of chaos try to estimate the so-called Lyapunov exponents as a way of characterising achaotic system. Nowadays quantifying chaos from time-series data through this kind of quantitative measure in a rigorous fashion is far from being a trivial exercise and poses a number of theoretical and practical challenges...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Estudios Estadísticos, leída el 05/11/2020