Simulating Analyzing And Animating Dynamical Systems

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Simulating Analyzing And Animating Dynamical Systems

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Author : Bard Ermentrout
language : en
Publisher: SIAM
Release Date : 2002-01-01

Simulating Analyzing And Animating Dynamical Systems written by Bard Ermentrout and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.

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.

Numerical Continuation Methods For Dynamical Systems

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Author : Bernd Krauskopf
language : en
Publisher: Springer
Release Date : 2007-11-06

Numerical Continuation Methods For Dynamical Systems written by Bernd Krauskopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-06 with Science categories.

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

Dynamical Systems Pdes And Networks For Biomedical Applications Mathematical Modeling Analysis And Simulations

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Author : André H. Erhardt
language : en
Publisher: Frontiers Media SA
Release Date : 2023-02-15

Dynamical Systems Pdes And Networks For Biomedical Applications Mathematical Modeling Analysis And Simulations written by André H. Erhardt and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-15 with Science categories.

Elements Of Applied Bifurcation Theory

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Author : Yuri Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Elements Of Applied Bifurcation Theory written by Yuri Kuznetsov 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 2013-03-09 with Mathematics categories.

The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense. The idea was to write a simple text that could serve as a seri ous introduction to the subject. Of course, the meaning of "simplicity" varies from person to person and from country to country. The word "introduction" contains even more ambiguity. To start reading this book, only a moder ate knowledge of linear algebra and calculus is required. Other preliminaries, qualified as "elementary" in modern mathematics, are explicitly formulated in the book. These include the Fredholm Alternative for linear systems and the multidimensional Implicit Function Theorem. Using these very limited tools, a framewo:k of notions, results, and methods is gradually built that allows one to read (and possibly write) scientific papers on bifurcations of nonlinear dynamical systems. Among other things, progress in the sciences means that mathematical results and methods that once were new become standard and routinely used by the research and development community. Hopefully, this edition of the book will contribute to this process. The book's structure has been kept intact. Most of the changes introduced reflect recent theoretical and software developments in which the author was involved. Important changes in the third edition can be summarized as follows. A new section devoted to the fold-flip bifurcation for maps has appeared in Chapter 9.

Algebraic Biology

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Author : Katsuhisa Horimoto
language : en
Publisher: Springer
Release Date : 2008-07-30

Algebraic Biology written by Katsuhisa Horimoto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-30 with Computers categories.

This volume contains the proceedings of the Third International Conference on Algebraic Biology (AB 2008). Jointly organized by the National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, and the Research Institute for Symbolic Computation (RISC), Hagenberg, Austria, it was held from July 31 to August 2, 2008 in the Castle of Hagenberg. Algebraic biology is an interdisciplinary forum for research on all aspects of applying symbolic computation in biology. The ?rst conference on algebraic biology (AB 2005) was held November 28–30, 2005 in Tokyo, the second during July 2–4, 2007 in Hagenberg. The AB conference series is intended as a bridge between life sciences and symbolic computation: On the one hand, new insights inbiologyarefoundbypowerfulsymbolicmethods;ontheotherhand,biological problems suggestnew algebraicstructures andalgorithms.While this pro?le has been established in the previous proceedings, the papers in the present volume demonstrate the continuous growth of algebraic biology. We received 27 submissions from 14 countries (Australia, Austria, Canada, China, Colombia, France, Germany, Italy, Japan, Norway, Russia, Switzerland, UK, USA), and 14 papers were accepted for publication. Each submission was assigned to at least three ProgramCommittee members, who carefully reviewed the papers, in many cases with the help of external referees. The reviews were discussedby the ProgramCommittee for oneweekvia the EasyChairconference management system.

Classical Methods In Ordinary Differential Equations

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Author : Stuart P. Hastings
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-12-15

Classical Methods In Ordinary Differential Equations written by Stuart P. Hastings and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-15 with Mathematics categories.

This text emphasizes rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behavior of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or traveling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed. The book gives complete classical proofs, while also emphasizing the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years. Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics.

From Molecules To Networks

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Author : John H. Byrne
language : en
Publisher: Academic Press
Release Date : 2014-05-23

From Molecules To Networks written by John H. Byrne and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-23 with Medical categories.

An understanding of the nervous system at virtually any level of analysis requires an understanding of its basic building block, the neuron. The third edition of From Molecules to Networks provides the solid foundation of the morphological, biochemical, and biophysical properties of nerve cells. In keeping with previous editions, the unique content focus on cellular and molecular neurobiology and related computational neuroscience is maintained and enhanced. All chapters have been thoroughly revised for this third edition to reflect the significant advances of the past five years. The new edition expands on the network aspects of cellular neurobiology by adding new coverage of specific research methods (e.g., patch-clamp electrophysiology, including applications for ion channel function and transmitter release; ligand binding; structural methods such as x-ray crystallography). Written and edited by leading experts in the field, the third edition completely and comprehensively updates all chapters of this unique textbook and insures that all references to primary research represent the latest results. - The first treatment of cellular and molecular neuroscience that includes an introduction to mathematical modeling and simulation approaches - 80% updated and new content - New Chapter on "Biophysics of Voltage-Gated Ion Channels" - New Chapter on "Synaptic Plasticity" - Includes a chapter on the Neurobiology of Disease - Highly referenced, comprehensive and quantitative - Full color, professional graphics throughout - All graphics are available in electronic version for teaching purposes

Neuroinformatics Of Large Scale Brain Modelling

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Author : John David Griffiths
language : en
Publisher: Frontiers Media SA
Release Date : 2022-11-10

Neuroinformatics Of Large Scale Brain Modelling written by John David Griffiths and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-10 with Science categories.

Deterministic Versus Stochastic Modelling In Biochemistry And Systems Biology

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Author : Paola Lecca
language : en
Publisher: Elsevier
Release Date : 2013-04-09

Deterministic Versus Stochastic Modelling In Biochemistry And Systems Biology written by Paola Lecca and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.

Stochastic kinetic methods are currently considered to be the most realistic and elegant means of representing and simulating the dynamics of biochemical and biological networks. Deterministic versus stochastic modelling in biochemistry and systems biology introduces and critically reviews the deterministic and stochastic foundations of biochemical kinetics, covering applied stochastic process theory for application in the field of modelling and simulation of biological processes at the molecular scale. Following an overview of deterministic chemical kinetics and the stochastic approach to biochemical kinetics, the book goes onto discuss the specifics of stochastic simulation algorithms, modelling in systems biology and the structure of biochemical models. Later chapters cover reaction-diffusion systems, and provide an analysis of the Kinfer and BlenX software systems. The final chapter looks at simulation of ecodynamics and food web dynamics. - Introduces mathematical concepts and formalisms of deterministic and stochastic modelling through clear and simple examples - Presents recently developed discrete stochastic formalisms for modelling biological systems and processes - Describes and applies stochastic simulation algorithms to implement a stochastic formulation of biochemical and biological kinetics

Nonlinear Dynamics In Computational Neuroscience

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Author : Fernando Corinto
language : en
Publisher: Springer
Release Date : 2018-06-19

Nonlinear Dynamics In Computational Neuroscience written by Fernando Corinto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-19 with Technology & Engineering categories.

This book provides an essential overview of computational neuroscience. It addresses a broad range of aspects, from physiology to nonlinear dynamical approaches to understanding neural computation, and from the simulation of brain circuits to the development of engineering devices and platforms for neuromorphic computation. Written by leading experts in such diverse fields as neuroscience, physics, psychology, neural engineering, cognitive science and applied mathematics, the book reflects the remarkable advances that have been made in the field of computational neuroscience, an emerging discipline devoted to the study of brain functions in terms of the information-processing properties of the structures forming the nervous system. The contents build on the workshop “Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT,” which was held in Torino, Italy in September 2015.