Multiple Time Scale Dynamical Systems

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Multiple Time Scale Dynamical Systems

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Author : Christopher K.R.T. Jones
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Multiple Time Scale Dynamical Systems written by Christopher K.R.T. Jones and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Multiple Time Scale Dynamics

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Author : Christian Kuehn
language : en
Publisher: Springer
Release Date : 2015-02-25

Multiple Time Scale Dynamics written by Christian Kuehn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-25 with Mathematics categories.

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.

Multiple Time Scale Dynamics

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Author : Christian Kuehn
language : en
Publisher: Springer
Release Date : 2015-03-06

Multiple Time Scale Dynamics written by Christian Kuehn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-06 with Mathematics categories.

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.

Topics In Multiple Time Scale Dynamics

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Author : Maximilian Engel
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-21

Topics In Multiple Time Scale Dynamics written by Maximilian Engel and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-21 with Mathematics categories.

This volume contains the proceedings of the BIRS Workshop "Topics in Multiple Time Scale Dynamics," held from November 27? December 2, 2022, at the Banff International Research Station, Banff, Alberta, Canada. The area of multiple-scale dynamics is rapidly evolving, marked by significant theoretical breakthroughs and practical applications. The workshop facilitated a convergence of experts from various sub-disciplines, encompassing topics like blow-up techniques for ordinary differential equations (ODEs), singular perturbation theory for stochastic differential equations (SDE), homogenization and averaging, slow-fast maps, numerical approaches, and network dynamics, including their applications in neuroscience and climate science. This volume provides a wide-ranging perspective on the current challenging subjects being explored in the field, including themes such as novel approaches to blowing-up and canard theory in unique contexts, complex multi-scale challenges in PDEs, and the role of stochasticity in multiple-scale systems.

Multiple Time Scales

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Author : Jeremiah U. Brackbill
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Multiple Time Scales written by Jeremiah U. Brackbill and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

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.

From Animals To Animats 8

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Author : Stefan Schaal
language : en
Publisher: MIT Press
Release Date : 2004

From Animals To Animats 8 written by Stefan Schaal and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.

New research on the adaptive behavior of natural and synthetic agents.

Control And Dynamic Systems V27

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Author : C.T. Leonides
language : en
Publisher: Elsevier
Release Date : 2012-12-02

Control And Dynamic Systems V27 written by C.T. Leonides and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Technology & Engineering categories.

Control and Dynamic Systems: Advances in Theory and Application, Volume 27: System Identification and Adaptive Control, Part 3 of 3 deals with system parameter identification and adaptive control. It presents useful techniques for adaptive control systems. This volume begins by presenting a powerful approach to multivariable model reference adaptive control based on the ideas and techniques of disturbance-accommodating control theory. It then discusses the modeling of biological systems; optimal control for air conditioning systems; linear programming for constrained multivariable process control; finite element approximation; development of irreducible state space singular systems; and discrete systems with multiple time scales. This book is an important reference for practitioners in the field who want a comprehensive source of techniques with significant applied implications.

Nonlinear Dynamics And Chaos

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Author : J Hogan
language : en
Publisher: CRC Press
Release Date : 2002-08-01

Nonlinear Dynamics And Chaos written by J Hogan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-01 with Mathematics categories.

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

A Dynamic Systems Approach To The Development Of Cognition And Action

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Author : Esther Thelen
language : en
Publisher: MIT Press
Release Date : 1994

A Dynamic Systems Approach To The Development Of Cognition And Action written by Esther Thelen and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Psychology categories.

A Dynamic Systems Approach to the Development of Cognition and Action presents a comprehensive and detailed theory of early human development based on the principles of dynamic systems theory. Beginning with their own research in motor, perceptual, and cognitive development, Thelen and Smith raise fundamental questions about prevailing assumptions in the field. They propose a new theory of the development of cognition and action, unifying recent advances in dynamic systems theory with current research in neuroscience and neural development. In particular, they show how by processes of exploration and selection, multimodal experiences form the bases for self-organizing perception-action categories. Thelen and Smith offer a radical alternative to current cognitive theory, both in their emphasis on dynamic representation and in their focus on processes of change. Among the first attempt to apply complexity theory to psychology, they suggest reinterpretations of several classic issues in early cognitive development. The book is divided into three sections. The first discusses the nature of developmental processes in general terms, the second covers dynamic principles in process and mechanism, and the third looks at how a dynamic theory can be applied to enduring puzzles of development. Cognitive Psychology series

Dislocations In Solids

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Author :
language : en
Publisher: Elsevier
Release Date : 2007-05-16

Dislocations In Solids written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-16 with Science categories.

Dislocations are lines of irregularity in the structure of a solid analogous to the bumps in a badly laid carpet. Like these bumps they can be easily moved, and they provide the most important mechanism by which the solid can be deformed. They also have a strong influence on crystal growth and on the electronic properties of semiconductors.·Influence of dislocations on piezoelectric behavior·New mechanisms for hardening in twinned crystals·Bringing theories of martensite transformation into agreement·Atomic scale motion of dislocations in electron microscopy·Dislocation patterns deduced from X-ray diffraction·Role of dislocations in friction·Dislocation motion in quasicrystals