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Bifurcation Analysis Of Multifrequency Patterns In Coupled Van Der Pol Oscillators
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Book Synopsis Mathematical Modeling by : Antonio Palacios
Download or read book Mathematical Modeling written by Antonio Palacios and published by Springer Nature. This book was released on 2022-09-19 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides qualitative and quantitative methods to analyze and better understand phenomena that change in space and time. An innovative approach is to incorporate ideas and methods from dynamical systems and equivariant bifurcation theory to model, analyze and predict the behavior of mathematical models. In addition, real-life data is incorporated in the derivation of certain models. For instance, the model for a fluxgate magnetometer includes experiments in support of the model. The book is intended for interdisciplinary scientists in STEM fields, who might be interested in learning the skills to derive a mathematical representation for explaining the evolution of a real system. Overall, the book could be adapted in undergraduate- and postgraduate-level courses, with students from various STEM fields, including: mathematics, physics, engineering and biology.
Book Synopsis Symmetry in Complex Network Systems by : Visarath In
Download or read book Symmetry in Complex Network Systems written by Visarath In and published by Springer. This book was released on 2017-09-05 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics. A general approach for their analysis has been to derive a detailed model of their individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in highly complicated models that are difficult to analyze even numerically. The alternative approach, while nonstandard, is not entirely new among the mathematics community. However, there is much less familiarity with the techniques of symmetry-breaking bifurcation, as they apply to the engineering, design and fabrication, of complex systems, in particular, nonlinear sensor devices with special emphasis on the conceptualization and development of new technologies of magnetic sensors such as fluxgate magnetometers and SQUID (Superconducting Quantum Interference Devices), E-- (electric-field) sensors, and communication and navigation systems that require multiple frequencies of operation, such as radar and antenna devices as well as gyroscopic systems.
Book Synopsis Computational Neuroscience by : James M. Bower
Download or read book Computational Neuroscience written by James M. Bower and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes papers presented at the Sixth Annual Computational Neurosci ence meeting (CNS*97) held in Big Sky, Montana, July 6-10, 1997. This collection includes 103 of the 196 papers presented at the meeting. Acceptance for meeting presentation was based on the peer review of preliminary papers originally submitted in January of 1997. The papers in this volume represent final versions of this work submitted in January of 1998. Taken together they provide a cross section of computational neuroscience and represent well the continued vitality and growth of this field. The meeting in Montana was unusual in several respects. First, to our knowledge it was the first international scientific meeting with opening ceremonies on horseback. Second, after five days of rigorous scientific discussion and debate, meeting participants were able to resolve all remaining conflicts in barrel race competitions. Otherwise the magnificence of Montana and the Big Sky Ski Resort assured that the meeting will not soon be forgotten. Scientifically, this volume once again represents the remarkable breadth of subjects that can be approached with computational tools. This volume and the continuing CNS meet ings make it clear that there is almost no subject or area of modem neuroscience research that is not appropriate for computational studies.
Book Synopsis Electrical & Electronics Abstracts by :
Download or read book Electrical & Electronics Abstracts written by and published by . This book was released on 1997 with total page 2240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiple Time Scale Dynamics by : Christian Kuehn
Download or read book Multiple Time Scale Dynamics written by Christian Kuehn and published by Springer. This book was released on 2015-02-25 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Balance for Nonlinear Vibration Problems by : Malte Krack
Download or read book Harmonic Balance for Nonlinear Vibration Problems written by Malte Krack and published by Springer. This book was released on 2019-03-23 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. Harmonic Balance is an approximation method for the computation of periodic solutions of nonlinear ordinary and differential-algebraic equations. It outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude. The method is widely used in the analysis of nonlinear systems, including structures, fluids and electric circuits. The book includes solved exercises which illustrate the advantages of Harmonic Balance over alternative methods as well as its limitations. The target audience primarily comprises graduate and post-graduate students, but the book may also be beneficial for research experts and practitioners in industry.
Book Synopsis Recipes for Continuation by : Harry Dankowicz
Download or read book Recipes for Continuation written by Harry Dankowicz and published by SIAM. This book was released on 2013-08-08 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical methodology of parameter continuation. It develops a systematic formalism for constructing and implementing abstract representations of continuation problems with equal emphasis on theoretical rigor, algorithm development and software engineering. The book demonstrates the use of fully developed toolbox templates for boundary-value problems to the analysis of periodic orbits, quasi-periodic invariant tori, and connecting orbits between equilibria and/or periodic orbits. The book contains extensive and fully-worked examples that illustrate the application of the MATLAB-based Computational Continuation Core (COCO) to cutting-edge research in applied dynamical systems. Many exercises and open-ended projects on both theoretical and algorithmic aspects of the material are provided, suitable for self-study and course assignments. It is intended for students and teachers of nonlinear dynamics and engineering at the advanced undergraduate or first-year graduate level, as well as practitioners engaged in modeling dynamical systems or software development.
Book Synopsis Rhythms of the Brain by : G. Buzsáki
Download or read book Rhythms of the Brain written by G. Buzsáki and published by Oxford University Press. This book was released on 2011 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of mechanisms in the brain that allow complicated things to happen in a coordinated fashion have produced some of the most spectacular discoveries in neuroscience. This book provides eloquent support for the idea that spontaneous neuron activity, far from being mere noise, is actually the source of our cognitive abilities. It takes a fresh look at the coevolution of structure and function in the mammalian brain, illustrating how self-emerged oscillatory timing is the brain's fundamental organizer of neuronal information. The small-world-like connectivity of the cerebral cortex allows for global computation on multiple spatial and temporal scales. The perpetual interactions among the multiple network oscillators keep cortical systems in a highly sensitive "metastable" state and provide energy-efficient synchronizing mechanisms via weak links. In a sequence of "cycles," György Buzsáki guides the reader from the physics of oscillations through neuronal assembly organization to complex cognitive processing and memory storage. His clear, fluid writing-accessible to any reader with some scientific knowledge-is supplemented by extensive footnotes and references that make it just as gratifying and instructive a read for the specialist. The coherent view of a single author who has been at the forefront of research in this exciting field, this volume is essential reading for anyone interested in our rapidly evolving understanding of the brain.
Book Synopsis The Symmetry Perspective by : Martin Golubitsky
Download or read book The Symmetry Perspective written by Martin Golubitsky and published by Birkhäuser. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
Book Synopsis Bifurcation and Symmetry by : BÖHMER
Download or read book Bifurcation and Symmetry written by BÖHMER and published by Birkhäuser. This book was released on 2013-03-08 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.
Book Synopsis Nonlinear Oscillations and Waves in Dynamical Systems by : P.S Landa
Download or read book Nonlinear Oscillations and Waves in Dynamical Systems written by P.S Landa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
Book Synopsis Simulating, Analyzing, and Animating Dynamical Systems by : Bard Ermentrout
Download or read book Simulating, Analyzing, and Animating Dynamical Systems written by Bard Ermentrout and published by SIAM. This book was released on 2002-01-01 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modeling techniques and methods for analyzing the resulting equations. Instructors, students, and researchers will all benefit from this book, which demonstrates how to use software tools to simulate and study sets of equations that arise in a variety of applications. Instructors will learn how to use computer software in their differential equations and modeling classes, while students will learn how to create animations of their equations that can be displayed on the World Wide Web. Researchers will be introduced to useful tricks that will allow them to take full advantage of XPPAUT's capabilities.
Book Synopsis International Aerospace Abstracts by :
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1998 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Coordination Dynamics: Issues and Trends by : Viktor K. Jirsa
Download or read book Coordination Dynamics: Issues and Trends written by Viktor K. Jirsa and published by Springer. This book was released on 2013-11-01 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together scientists from all over the world who have defined and developed the field of Coordination Dynamics. Grounded in the concepts of self-organization and the tools of nonlinear dynamics, appropriately extended to handle informational aspects of living things, Coordination Dynamics aims to understand the coordinated functioning of a variety of different systems at multiple levels of description. The book addresses the themes of Coordination Dynamics and Dynamic Patterns in the context of the following topics: Coordination of Brain and Behavior, Perception-Action Coupling, Control, Posture, Learning, Intention, Attention, and Cognition.
Author :N. Sri Namachchivaya Publisher :Springer Science & Business Media ISBN 13 :9781402014710 Total Pages :498 pages Book Rating :4.0/5 (147 download)
Book Synopsis IUTAM Symposium on Nonlinear Stochastic Dynamics by : N. Sri Namachchivaya
Download or read book IUTAM Symposium on Nonlinear Stochastic Dynamics written by N. Sri Namachchivaya and published by Springer Science & Business Media. This book was released on 2003-11-30 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics. The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling. For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.
