Synchronization of Oscillatory Networks in Terms of Global Variables - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Synchronization of Oscillatory Networks in Terms of Global Variables write by . This book was released on 2015. Synchronization of Oscillatory Networks in Terms of Global Variables available in PDF, EPUB and Kindle. Synchronization of large ensembles of oscillators is an omnipresent phenomenon observed in different fields of science like physics, engineering, life sciences, etc. The most simple setup is that of globally coupled phase oscillators, where all the oscillators contribute to a global field which acts on all oscillators. This formulation of the problem was pioneered by Winfree and Kuramoto. Such a setup gives a possibility for the analysis of these systems in terms of global variables. In this work we describe nontrivial collective dynamics in oscillator populations coupled via mean fields in terms of global variables. We consider problems which cannot be directly reduced to standard Kuramoto and Winfree models. In the first part of the thesis we adopt a method introduced by Watanabe and Strogatz. The main idea is that the system of identical oscillators of particular type can be described by a low-dimensional system of global equations. This approach enables us to perform a complete analytical analysis for a special but vast set of initial conditions. Furthermore, we show how the approach can be expanded for some nonidentical systems. We apply the Watanabe-Strogatz approach to arrays of Josephson junctions and systems of identical phase oscillators with leader-type coupling. In the next parts of the thesis we consider the self-consistent mean-field theory method that can be applied to general nonidentical globally coupled systems of oscillators both with or without noise. For considered systems a regime, where the global field rotates uniformly, is the most important one. With the help of this approach such solutions of the self-consistency equation for an arbitrary distribution of frequencies and coupling parameters can be found analytically in the parametric form, both for noise-free and noisy cases. We apply this method to deterministic Kuramoto-type model with generic coupling and an ensemble of spatially distributed oscillators with leader-type coupling. Furthermore, with the proposed self-consistent approach we fully characterize rotating wave solutions of noisy Kuramoto-type model with generic coupling and an ensemble of noisy oscillators with bi-harmonic coupling. Whenever possible, a complete analysis of global dynamics is performed and compared with direct numerical simulations of large populations
Synchronization in Oscillatory Networks
Synchronization in Oscillatory Networks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Synchronization in Oscillatory Networks write by Grigory V. Osipov. This book was released on 2007-08-10. Synchronization in Oscillatory Networks available in PDF, EPUB and Kindle. This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or even the heart muscle, to name but a few. The book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.
Synchronization of Oscillators and Global Output Regulation for Rigid Body Systems
Synchronization of Oscillators and Global Output Regulation for Rigid Body Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Synchronization of Oscillators and Global Output Regulation for Rigid Body Systems write by Gerd Simon Schmidt. This book was released on 2014. Synchronization of Oscillators and Global Output Regulation for Rigid Body Systems available in PDF, EPUB and Kindle. The investigation of nonlinear dynamis in physical and engineering systems from the point of view of systems and control theory is important to develop better engineering systems. Synchronization of oscillators and output regulation for rigid body systems are two problem classes which are inherently nonlinear and are of great importance in applications. This thesis contains novel results for both problem classes. In the case of sychronization of oscillators we consider two different system classes and give sufficient or necessary conditions for synchronization. In the case of the output regulation problems for rigid body systems we provide a new two-step control design procedure, a detailed analysis for the error dynamics and an application scenario for satellite control. A highlight of the thesis is a new separation principle which is the underlying principle of the two-step design procedure for the output regulation problem.
Synchronization
Synchronization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Synchronization write by Alexander Balanov. This book was released on 2008-11-23. Synchronization available in PDF, EPUB and Kindle. This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.
Oscillatory Neural Networks
Oscillatory Neural Networks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Oscillatory Neural Networks write by Margarita G. Kuzmina. This book was released on 2013-11-27. Oscillatory Neural Networks available in PDF, EPUB and Kindle. Understanding of the human brain functioning currently represents a challenging problem. In contrast to usual serial computers and complicated hierarchically organized artificial man-made systems, decentralized, parallel and distributed information processing principles are inherent to the brain. Besides adaptation and learning, which play a crucial role in brain functioning, oscillatory neural activity, synchronization and resonance accompany the brain work. Neural-like oscillatory network models, designed by the authors for image processing, allow to elucidate the capabilities of dynamical, synchronization-based types of image processing, presumably exploited by the brain. The oscillatory network models, studied by means of computer modeling and qualitative analysis, are presented and discussed in the book. Some other problems of parallel distributed information processing are also considered, such as a recall process from network memory for large-scale recurrent associative memory neural networks, performance of oscillatory networks of associative memory, dynamical oscillatory network methods of image processing with synchronization-based performance, optical parallel information processing based on the nonlinear optical phenomenon of photon echo, and modeling random electric fields of quasi-monochromatic polarized light beams using systems of superposed stochastic oscillators. This makes the book highly interesting to researchers dealing with various aspects of parallel information processing.
