Multiple Time Scale Dynamics

Author : Christian Kuehn
Publisher : Springer
ISBN 13 : 3319123165
Total Pages : 816 pages
Book Rating : 4.65/5 ( download)

DOWNLOAD NOW!

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.

Author : Christopher K.R.T. Jones
Publisher : Springer Science & Business Media
ISBN 13 : 1461301173
Total Pages : 278 pages
Book Rating : 4.72/5 ( download)

DOWNLOAD NOW!

Download or read book Multiple-Time-Scale Dynamical Systems written by Christopher K.R.T. Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.

Author : Jeremiah U. Brackbill
Publisher : Academic Press
ISBN 13 : 1483257568
Total Pages : 457 pages
Book Rating : 4.63/5 ( download)

DOWNLOAD NOW!

Download or read book Multiple Time Scales written by Jeremiah U. Brackbill and published by Academic Press. This book was released on 2014-05-10 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.

Author : Ying Wu
Publisher : Frontiers Media SA
ISBN 13 : 2832535569
Total Pages : 120 pages
Book Rating : 4.61/5 ( download)

DOWNLOAD NOW!

Download or read book Multi-Scale Dynamics Modeling of Brain Physiological Functions and Pathological Mechanisms written by Ying Wu and published by Frontiers Media SA. This book was released on 2023-10-09 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mechanisms of brain physiological functions and pathological mechanisms are crucial for us to understand how the brain works in the normal function such as memory, information processing and attentional perception, or in pathological conditions such as epilepsy, Parkinson's disease, and Alzheimer's diseases. These brain physiological functions and pathological mechanisms generally involve multiple spatial scales of brains, ranging from micro molecules, cellular channels, and meso-scale neuronal networks to the brain regions. To comprehensively understand the neural mechanisms of brain physiological functions and pathological mechanisms, multiple-scale investigations are essential to carry, involving neuronal circuit modeling, neural field modeling, large-scale modeling, data-driven complex network modeling, etc.

Author : Bernhelm Booss
Publisher : Springer Nature
ISBN 13 : 3031280490
Total Pages : 477 pages
Book Rating : 4.98/5 ( download)

DOWNLOAD NOW!

Download or read book Multiplicity of Time Scales in Complex Systems written by Bernhelm Booss and published by Springer Nature. This book was released on 2024 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This highly interdisciplinary volume brings together a carefully curated set of case studies examining complex systems with multiple time scales (MTS) across a variety of fields: materials science, epidemiology, cell physiology, mathematics, climatology, energy transition planning, ecology, economics, sociology, history, and cultural studies. The book addresses the vast diversity of interacting processes underlying the behaviour of different complex systems, highlighting the multiplicity of characteristic time scales that are a common feature of many and showcases a rich variety of methodologies across disciplinary boundaries. Self-organizing, out-of-equilibrium, ever-evolving systems are ubiquitous in the natural and social world. Examples include the climate, ecosystems, living cells, epidemics, the human brain, and many socio-economic systems across history. Their dynamical behaviour poses great challenges in the pressing context of the climate crisis, since they may involve nonlinearities, feedback loops, and the emergence of spatial-temporal patterns, portrayed by resilience or instability, plasticity or rigidity; bifurcations, thresholds and tipping points; burst-in excitation or slow relaxation, and worlds of other asymptotic behaviour, hysteresis, and resistance to change. Chapters can be read individually by the reader with special interest in such behaviours of particular complex systems or in specific disciplinary perspectives. Read together, however, the case studies, opinion pieces, and meta-studies on MTS systems presented and analysed here combine to give the reader insights that are more than the sum of the book's individual chapters, as surprising similarities become apparent in seemingly disparate and unconnected systems. MTS systems call into question naïve perceptions of time and complexity, moving beyond conventional ways of description, analysis, understanding, modelling, numerical prediction, and prescription of the world around us. This edited collection presents new ways of forecasting, introduces new means of control, and - perhaps as the most demanding task - it singles out a sustainable description of an MTS system under observation, offering a more nuanced interpretation of the floods of quantitative data and images made available by high- and low-frequency measurement tools in our unprecedented era of information flows

Author : Verica Radisavljević-Gajić
Publisher : Springer
ISBN 13 : 3030103897
Total Pages : 214 pages
Book Rating : 4.97/5 ( download)

DOWNLOAD NOW!

Download or read book Multi-Stage and Multi-Time Scale Feedback Control of Linear Systems with Applications to Fuel Cells written by Verica Radisavljević-Gajić and published by Springer. This book was released on 2019-02-12 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive study of multi-stage and multi-time scale design of feedback controllers for linear dynamic systems. It examines different types of controllers as can be designed for different parts of the system (subsystems) using corresponding feedback gains obtained by performing calculations (design) only with subsystem (reduced-order) matrices.The advantages of the multi-stage/multi-time scale design are presented and conditions for implementation of these controllers are established. Complete derivations and corresponding design techniques are presented for two-stage/two-time-scale, three-stage/three-time scale, and four-stage/four-time-scale systems. The techniques developed have potential applications to a large number of real physical systems. The design techniques are demonstrated on examples of mathematical models of fuel cells, especially the proton exchange membrane fuel cell.

Author : J Hogan
Publisher : CRC Press
ISBN 13 : 1420033832
Total Pages : 370 pages
Book Rating : 4.30/5 ( download)

DOWNLOAD NOW!

Download or read book Nonlinear Dynamics and Chaos written by J Hogan and published by CRC Press. This book was released on 2002-08-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such sys

Author : Alexander N. Gorban
Publisher : Springer Science & Business Media
ISBN 13 : 3540358889
Total Pages : 554 pages
Book Rating : 4.86/5 ( download)

DOWNLOAD NOW!

Download or read book Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena written by Alexander N. Gorban and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.

Author : Wulfram Gerstner
Publisher : Cambridge University Press
ISBN 13 : 1107060834
Total Pages : 591 pages
Book Rating : 4.38/5 ( download)

DOWNLOAD NOW!

Download or read book Neuronal Dynamics written by Wulfram Gerstner and published by Cambridge University Press. This book was released on 2014-07-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.

Author : Anshu Narang-Siddarth
Publisher : SIAM
ISBN 13 : 1611973333
Total Pages : 231 pages
Book Rating : 4.34/5 ( download)

DOWNLOAD NOW!

Download or read book Nonlinear Time Scale Systems in Standard and Nonstandard Forms written by Anshu Narang-Siddarth and published by SIAM. This book was released on 2014-04-22 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces key concepts for systematically controlling engineering systems that possess interacting phenomena occurring at widely different speeds. The aim is to present the reader with control techniques that extend the benefits of model reduction of singular perturbation theory to a larger class of nonlinear dynamical systems. New results and relevant background are presented through insightful examples that cover a wide range of applications from different branches of engineering. This book is unique because it presents a new perspective on existing control methods and thus broadens their application to a larger class of nonlinear dynamical systems. It also discusses general rather than problem-specific developments to certain applications or disciplines in order to provide control engineers with useful analytical tools, and it addresses new control problems using singular perturbation methods, including closed-form results for control of nonminimum phase systems.