Simulating, Analyzing, and Animating Dynamical Systems PDF Download
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Author: Bard Ermentrout
Publisher: SIAM
ISBN: 0898715067
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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.
Author: Bard Ermentrout
Publisher: SIAM
ISBN: 0898715067
Category : Mathematics
Languages : en
Pages : 298
Get Book Here
Book Description
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.
Author: Bard Ermentrout
Publisher: SIAM
ISBN: 9780898718195
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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.
Author: Bernd Krauskopf
Publisher: Springer
ISBN: 1402063563
Category : Science
Languages : en
Pages : 411
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Book Description
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.
Author: André H. Erhardt
Publisher: Frontiers Media SA
ISBN: 2832514588
Category : Science
Languages : en
Pages : 209
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Book Description
Author: Willy J. F. Govaerts
Publisher: SIAM
ISBN: 9780898719543
Category : Mathematics
Languages : en
Pages : 384
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Book Description
Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.
Author: Eugene M. Izhikevich
Publisher: MIT Press
ISBN: 0262514206
Category : Medical
Languages : en
Pages : 459
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Book Description
Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.
Author: Shinji Doi
Publisher: Springer Science & Business Media
ISBN: 4431538623
Category : Technology & Engineering
Languages : en
Pages : 159
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Book Description
Biological systems inherently possess much ambiguity or uncertainty. Computational electrophysiology is the one area, from among the vast and rapidly growing discipline of computational and systems biology, in which computational or mathematical models have succeeded. This textbook provides a practical and quick guide to both computational electrophysiology and numerical bifurcation analysis. Bifurcation analysis is a very powerful tool for the analysis of such highly nonlinear biological systems. Bifurcation theory provides a way to analyze the effect of a parameter change on a system and to detect a critical parameter value when the qualitative nature of the system changes. Included in this work are many examples of numerical computations of bifurcation analysis of various models as well as mathematical models with different abstraction levels from neuroscience and electrophysiology. This volume will benefit graduate and undergraduate students as well as researchers in diverse fields of science.
Author: Arpad Kelemen
Publisher: Springer Science & Business Media
ISBN: 3540768025
Category : Computers
Languages : en
Pages : 337
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Book Description
Bioinformatics involve the creation and advancement of algorithms using techniques including computational intelligence, applied mathematics and statistics, informatics, and biochemistry to solve biological problems usually on the molecular level. This book deals with the application of computational intelligence in bioinformatics. Addressing the various issues of bioinformatics using different computational intelligence approaches is the novelty of this edited volume.
Author: Dimitri Breda
Publisher: Springer Nature
ISBN: 3031011295
Category : Science
Languages : en
Pages : 369
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Book Description
This book gathers contributions on analytical, numerical, and application aspects of time-delay systems, under the paradigm of control theory, and discusses recent advances in these different contexts, also highlighting the interdisciplinary connections. The book will serve as a useful tool for graduate students and researchers in the fields of dynamical systems, automatic control, numerical methods, and functional analysis.
Author: Jinhu Lü
Publisher: Springer Nature
ISBN: 981159144X
Category : Science
Languages : en
Pages : 464
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Book Description
This book addresses a number of questions from the perspective of complex systems: How can we quantitatively understand the life phenomena? How can we model life systems as complex bio-molecular networks? Are there any methods to clarify the relationships among the structures, dynamics and functions of bio-molecular networks? How can we statistically analyse large-scale bio-molecular networks? Focusing on the modeling and analysis of bio-molecular networks, the book presents various sophisticated mathematical and statistical approaches. The life system can be described using various levels of bio-molecular networks, including gene regulatory networks, and protein-protein interaction networks. It first provides an overview of approaches to reconstruct various bio-molecular networks, and then discusses the modeling and dynamical analysis of simple genetic circuits, coupled genetic circuits, middle-sized and large-scale biological networks, clarifying the relationships between the structures, dynamics and functions of the networks covered. In the context of large-scale bio-molecular networks, it introduces a number of statistical methods for exploring important bioinformatics applications, including the identification of significant bio-molecules for network medicine and genetic engineering. Lastly, the book describes various state-of-art statistical methods for analysing omics data generated by high-throughput sequencing. This book is a valuable resource for readers interested in applying systems biology, dynamical systems or complex networks to explore the truth of nature.
