A Qualitative Study Of The Behavior Of Dynamic Nonlinear Networks
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| Author | : Leonid P. Shilnikov |
| Publisher | : World Scientific |
| Total Pages | : 420 |
| Release | : 1998 |
| Genre | : Science |
| ISBN | : 9789810233822 |
Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
| Author | : Leon O. Chua |
| Publisher | : World Scientific |
| Total Pages | : 362 |
| Release | : 1998 |
| Genre | : Computers |
| ISBN | : 9789810234836 |
Revolutionary and original, this treatise presents a new paradigm of Emergence and Complexity, with applications drawn from numerous disciplines, including artificial life, biology, chemistry, computation, physics, image processing, information science, etc. CNN is an acronym for Cellular Neural Networks when used in the context of brain science, or Cellular Nonlinear Networks, when used in the context of emergence and complexity. A CNN is modeled by cells and interactions: cells are defined as dynamical systems and interactions are defined via coupling laws. The CNN paradigm is a universal Turing machine and includes cellular automata and lattice dynamical systems as special cases. While the CNN paradigm is an example of Reductionism par excellence, the true origin of emergence and complexity is traced to a much deeper new concept called local activity. The numerous complex phenomena unified under this mathematically precise principle include self organization, dissipative structures, synergetics, order from disorder, far-from-thermodynamic equilibrium, collective behaviors, edge of chaos, etc. Written with a high level of exposition, this completely self-contained monograph is profusely illustrated with over 200 stunning color illustrations of emergent phenomena.
| Author | : |
| Publisher | : |
| Total Pages | : 1572 |
| Release | : 1992 |
| Genre | : Aeronautics |
| ISBN | : |
| Author | : Bharathwaj Muthuswamy |
| Publisher | : Springer |
| Total Pages | : 373 |
| Release | : 2018-10-26 |
| Genre | : Technology & Engineering |
| ISBN | : 3319673254 |
This course-based text revisits classic concepts in nonlinear circuit theory from a very much introductory point of view: the presentation is completely self-contained and does not assume any prior knowledge of circuit theory. It is simply assumed that readers have taken a first-year undergraduate course in differential and integral calculus, along with an elementary physics course in classical mechanics and electrodynamics. Further, it discusses topics not typically found in standard textbooks, such as nonlinear operational amplifier circuits, nonlinear chaotic circuits and memristor networks. Each chapter includes a set of illustrative and worked examples, along with end-of-chapter exercises and lab exercises using the QUCS open-source circuit simulator. Solutions and other material are provided on the YouTube channel created for this book by the authors.
| Author | : Ricardo Riaza |
| Publisher | : World Scientific |
| Total Pages | : 345 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9812791817 |
Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory.Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems. Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models.
| Author | : Chai Wah Wu |
| Publisher | : World Scientific |
| Total Pages | : 192 |
| Release | : 2002 |
| Genre | : Science |
| ISBN | : 9789810247133 |
Studies synchronization of coupled chaotic circuits and systems, as well as its applications.
| Author | : Chai Wah Wu |
| Publisher | : World Scientific |
| Total Pages | : 168 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9812709746 |
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area. Sample Chapter(s). Chapter 1: Introduction (76 KB). Contents: Graphs, Networks, Laplacian Matrices and Algebraic Connectivity; Graph Models; Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems; Synchronization in Networks of Coupled Discrete-Time Systems; Synchronization in Network of Systems with Linear Dynamics; Agreement and Consensus Problems in Groups of Interacting Agents. Readership: Graduate students and researchers in physics, applied mathematics and engineering.
| Author | : M.A. van Wyk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 489 |
| Release | : 2013-06-29 |
| Genre | : Technology & Engineering |
| ISBN | : 9401589216 |
Many dynamical systems in physics, chemistry and biology exhibit complex be haviour. The apparently random motion of a fluid is the best known example. How ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla tors is also included. End of proofs and examples are indicated by •. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: MVANWYK@TSAMAIL. TRSA. AC. ZA Email address of the first author: WHS@RAU3. RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.
| Author | : |
| Publisher | : |
| Total Pages | : 490 |
| Release | : |
| Genre | : Electrical engineering |
| ISBN | : |
| Author | : Alexandru Gabriel Gheorghe |
| Publisher | : CRC Press |
| Total Pages | : 212 |
| Release | : 2022-09-01 |
| Genre | : Technology & Engineering |
| ISBN | : 1000794083 |
New Topics in Simulation and Modeling of RF Circuits addresses two main topics: simulation of RF circuits and new models of nonlinear power BAW resonators and filters.Since RF circuits have several unique features, and all analysis methods are based on the circuit essential properties, the book begins by describing the properties of RF circuits, characterization of circuits with customary and uncustomary behavior and some theorems of solutions existence and uniqueness for dynamic nonlinear circuits. Thereafter, the main time domain and frequency domain analysis methods for RF circuits are presented. The advantages and disadvantages of each method have been highlighted, and an algorithm for the time step choice in transient analysis based on energy balance errors is also presented. Lastly, the final part contains some nonlinear circuit models of power BAW resonators. The behavioral models for the time domain analysis are simple circuits containing weakly nonlinear elements. The behavioral models for frequency domain analysis are based on the measured values of the frequency dependent S parameters for a set of incident powers. S parameters corresponding to certain intermodulation products of practical interest are also considered. The physical models contain artificial transmission lines with nonlinear circuit elements corresponding to mechanical and electrical nonlinearities.
