Download or read book Coarse-grained Models of Nonlinear Oscillators written by Navendu Patil and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In many practical situations, time series data are gathered and used to gain an understanding of the dynamics of a complex physical system. Whether the result of experimental measurements or numerical simulations, it is of particular importance to use such data to provide a model-based and objective quantification of the dynamical complexity of a system, which, together with a measure of its stochasticity, determine fundamental limits to the system's predictability. However, a number of approaches for estimating complexity are based on information theory and require sequences of coarse-grained, or more specifically, discrete observables, which are not usually directly available, and typically have to be generated from continuous-valued discrete-time series.In this work, we obtain discrete observables for systems, whose underlying generating mechanism is deterministic chaos, solely from their time series data. We devise a selection procedure to pick good observables from a candidate set, which have a simple structure in the space of continuous observations, and also remain particularly faithful to the original time series measurements without much loss of the relevant information. Using coarse-grained observables, we build computational models, which while being minimal in a specific sense, are in turn capable of statistically reproducing input sequence of these observables with high likelihood on average, at par with its true probability. From these coarse-grained, computational models, we then calculate information-theoretic quantities that distinguish apparent randomness from the deterministic structure of the system dynamics, as hidden in the time series data and captured by its discrete observables. Using these measures, we quantify the interaction effect of the external stochastic fluctuations with the underlying deterministic chaotic behavior of the driven nonlinear oscillators. We confirm the transition in the measure of randomness as a function of the noise level, from almost constant to a significantly high power-law growth regime. Finally, we study the noise-induced transitions of stable periodic orbits as part of the major problem of distinguishing chaos from noise, using noisy experimental measurements alone. We find that the possibility of such distinction is dependent on the amplitude of external stochastic fluctuations and also, to an extent, on the choice of coarse-grained observables.