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"Nonlinear theories"
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Nonlinear system identification : NARMAX methods in the time, frequency, and spatio-temporal domains
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice.
Includes coverage of:
* The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model
* The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term
* Statistical and qualitative model validation methods that can be applied to any model class
* Generalised frequency response functions which provide significant insight into nonlinear behaviours
* A completely new class of filters that can move, split, spread, and focus energy
* The response spectrum map and the study of sub harmonic and severely nonlinear systems
* Algorithms that can track rapid time variation in both linear and nonlinear systems
* The important class of spatio-temporal systems that evolve over both space and time
* Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included
to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems
NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems.
This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.
eBook
Conformal Graph Directed Markov Systems on Carnot Groups
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
eBook
Neural control engineering : the emerging intersection between control theory and neuroscience
How powerful new methods in nonlinear control engineering can be applied to neuroscience, from fundamental model formulation to advanced medical applications.Over the past sixty years, powerful methods of model-based control engineering have been responsible for such dramatic advances in engineering systems as autolanding aircraft, autonomous vehicles, and even weather forecasting. Over those same decades, our models of the nervous system have evolved from single-cell membranes to neuronal networks to large-scale models of the human brain. Yet until recently control theory was completely inapplicable to the types of nonlinear models being developed in neuroscience. The revolution in nonlinear control engineering in the late 1990s has made the intersection of control theory and neuroscience possible. In Neural Control Engineering, Steven Schiff seeks to bridge the two fields, examining the application of new methods in nonlinear control engineering to neuroscience. After presenting extensive material on formulating computational neuroscience models in a control environment-including some fundamentals of the algorithms helpful in crossing the divide from intuition to effective application-Schiff examines a range of applications, including brain-machine interfaces and neural stimulation. He reports on research that he and his colleagues have undertaken showing that nonlinear control theory methods can be applied to models of single cells, small neuronal networks, and large-scale networks in disease states of Parkinson's disease and epilepsy. With Neural Control Engineering the reader acquires a working knowledge of the fundamentals of control theory and computational neuroscience sufficient not only to understand the literature in this trandisciplinary area but also to begin working to advance the field. The book will serve as an essential guide for scientists in either biology or engineering and for physicians who wish to gain expertise in these areas.
eBook
Nonlinear Modeling of Economic and Financial Time-Series
Within the subprime crisis (2007) and the recent global financial crisis of 2008-2009, we have observed significant decline, corrections and structural changes in most US and European financial markets. Furthermore, it seems that this crisis has been rapidly transmitted toward the most developed and emerging countries and has strongly affected the whole economy. This volume aims to present recent researches in linear and nonlinear modelling of economic and financial time-series. The several discussions of empirical results of its chapters clearly help to improve the understanding of the financial mechanisms inherent to this crisis. They also yield an important overview on the sources of the financial crisis and its main economic and financial consequences. The book provides the audience a comprehensive understanding of financial and economic dynamics in various aspects using modern financial econometric methods. It addresses the empirical techniques needed by economic agents to analyze the dynamics of these markets and illustrates how they can be applied to the actual data. It also presents and discusses new research findings and their implications.
eBook
Nonlinear Dynamics
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation.
eBook