Nonlinear measures and dynamics from time series data

Abstract

Our attempts to understand the dynamics of natural systems often rely on the observations or average responses of the system The science of extracting information from this time series of observations forms the area of time series analysis The underlying dynamics of natural systems is nonlinear and therefore complex This nonlinearity leaves signatures in the dynamics of the system captured by the time series of its variables Nonlinear time series analysis strives to seek and interpret these signatures in order to capture the nature of the underlying dynamics This exercise is complicated by the presence of various shortcomings of real world data Some of the primary problems we encounter in this respect are noise data gaps and finite size of data This thesis attempts to address these problems in the context of nonlinear time series analysis The origins of dynamical systems theory can be traced back to the celestial Many of the ideas of this theory were developed while trying to address the three body problem Subsequently nonlinear dynamics has found applications in many fields of astrophysics These include stellar pulsations accretion disc physics galactic models and so on The use of time series analysis in astrophysics has been limited in the past due to the absence of long continuous and high quality datasets The advent of space telescopes has begun to overcome some of these problems Subsequently period doubling chaotic and strange non chaotic behavior etc have been observed in a large number of stars This thesis aims to explore the dynamics of variable stars in more detail seeking out signatures of nonlinearity and chaos in various scenarios After exploring the basics of nonlinear time series analysis and the physics of variable stars we proceed to address the issues commonly encountered in the nonlinear time series analysis of real world data We identify three main issues in this context namely the presence of datagaps noise and finite sizes of data We start by analyzi newline newline