The Fitzhugh Nagumo Model

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The FitzHugh-Nagumo Model

C. Rocsoreanu,A. Georgescu,N. Giurgiteanu
The FitzHugh Nagumo Model Book PDF

Author : C. Rocsoreanu,A. Georgescu,N. Giurgiteanu
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401595483

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The FitzHugh-Nagumo Model by C. Rocsoreanu,A. Georgescu,N. Giurgiteanu Pdf

The present monograph analyses the FitzHugh-Nagumo (F-N) model Le. , the Cauchy problem for some generalized Van der Pol equation depending on three real parameters a, band c. This model, given in (1. 1. 17), governs the initiation of the cardiac impulse. The presence of the three parameters leads to a large variety of dy namics, each of them responsible for a specific functioning of the heart. For physiologists it is highly desirable to have aglobai view of all possible qualitatively distinct responses of the F-N model for all values of the pa rameters. This reduces to the knowledge of the global bifurcation diagram. So far, only a few partial results appeared and they were spread through out the literature. Our work provides a more or less complete theoretical and numerical investigation of the complex phase dynamics and bifurca tions associated with the F-N dynamical system. This study includes the static and dynamic bifurcations generated by the variation of a, band c and the corresponding oscillations, of special interest for applications. It enables one to predict all possible types of initiations of heart beats and the mechanism of transformation of some types of oscillations into others by following the dynamics along transient phase space trajectories. Of course, all these results hold for the F-N model. The global phase space picture enables one to determine the domain of validity of this model.

Encyclopedia of Computational Neuroscience

Dieter Jäger,Ranu Jung
Encyclopedia of Computational Neuroscience Book PDF

Author : Dieter Jäger,Ranu Jung
Publisher : Springer
Page : 3663 pages
File Size : 43,5 Mb
Release : 2022-04-26
Category : Medical
ISBN : 107161004X

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Encyclopedia of Computational Neuroscience by Dieter Jäger,Ranu Jung Pdf

The annual Computational Neuroscience Meeting (CNS) began in 1990 as a small workshop called Analysis and Modeling of Neural Systems. The goal of the workshop was to explore the boundary between neuroscience and computation. Riding on the success of several seminal papers, physicists had made "Neural Networks" fashionable, and soon the quantitative methods used in these abstract model networks started permeating the methods and ideas of experimental neuroscientists. Although experimental neurophysiological approaches provided many advances, it became increasingly evident that mathematical and computational techniques would be required to achieve a comprehensive and quantitative understanding of neural system function. “Computational Neuroscience” emerged to complement experimental neurophysiology. The Encyclopedia of Computational Neuroscience, published in conjunction with the Organization for Computational Neuroscience, will be an extensive reference work consultable by both researchers and graduate level students. It will be a dynamic, living reference, updatable and containing linkouts and multimedia content whenever relevant.

Modeling Dynamic Biological Systems

Bruce Hannon,Matthias Ruth
Modeling Dynamic Biological Systems Book PDF

Author : Bruce Hannon,Matthias Ruth
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461206514

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Modeling Dynamic Biological Systems by Bruce Hannon,Matthias Ruth Pdf

Models help us understand the dynamics of real-world processes by using the computer to mimic the actual forces that are known or assumed to result in a system's behavior. This book does not require a substantial background in mathematics or computer science.

Dynamical Systems in Neuroscience

Eugene M. Izhikevich
Dynamical Systems in Neuroscience Book PDF

Author : Eugene M. Izhikevich
Publisher : MIT Press
Page : 459 pages
File Size : 50,9 Mb
Release : 2010-01-22
Category : Medical
ISBN : 9780262514200

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Dynamical Systems in Neuroscience by Eugene M. Izhikevich Pdf

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.

Neuronal Dynamics

Wulfram Gerstner,Werner M. Kistler,Richard Naud,Liam Paninski
Neuronal Dynamics Book PDF

Author : Wulfram Gerstner,Werner M. Kistler,Richard Naud,Liam Paninski
Publisher : Cambridge University Press
Page : 591 pages
File Size : 40,9 Mb
Release : 2014-07-24
Category : Computers
ISBN : 9781107060838

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Neuronal Dynamics by Wulfram Gerstner,Werner M. Kistler,Richard Naud,Liam Paninski Pdf

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.

Pattern Formation and Dynamics in Nonequilibrium Systems

Michael Cross,Henry Greenside
Pattern Formation and Dynamics in Nonequilibrium Systems Book PDF

Author : Michael Cross,Henry Greenside
Publisher : Cambridge University Press
Page : 547 pages
File Size : 46,7 Mb
Release : 2009-07-16
Category : Mathematics
ISBN : 9780521770507

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Pattern Formation and Dynamics in Nonequilibrium Systems by Michael Cross,Henry Greenside Pdf

An account of how complex patterns form in sustained nonequilibrium systems; for graduate students in biology, chemistry, engineering, mathematics, and physics.

MATLAB for Neuroscientists

Pascal Wallisch,Michael E. Lusignan,Marc D. Benayoun,Tanya I. Baker,Adam Seth Dickey,Nicholas G. Hatsopoulos
MATLAB for Neuroscientists Book PDF

Author : Pascal Wallisch,Michael E. Lusignan,Marc D. Benayoun,Tanya I. Baker,Adam Seth Dickey,Nicholas G. Hatsopoulos
Publisher : Academic Press
Page : 570 pages
File Size : 49,6 Mb
Release : 2014-01-09
Category : Computers
ISBN : 9780123838377

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MATLAB for Neuroscientists by Pascal Wallisch,Michael E. Lusignan,Marc D. Benayoun,Tanya I. Baker,Adam Seth Dickey,Nicholas G. Hatsopoulos Pdf

MATLAB for Neuroscientists serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that a wide variety of computational problems can be addressed in a single programming environment. This updated edition features additional material on the creation of visual stimuli, advanced psychophysics, analysis of LFP data, choice probabilities, synchrony, and advanced spectral analysis. Users at a variety of levels—advanced undergraduates, beginning graduate students, and researchers looking to modernize their skills—will learn to design and implement their own analytical tools, and gain the fluency required to meet the computational needs of neuroscience practitioners. The first complete volume on MATLAB focusing on neuroscience and psychology applications Problem-based approach with many examples from neuroscience and cognitive psychology using real data Illustrated in full color throughout Careful tutorial approach, by authors who are award-winning educators with strong teaching experience

Differential Equations with Applications to Biology

Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu
Differential Equations with Applications to Biology Book PDF

Author : Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu
Publisher : American Mathematical Soc.
Page : 521 pages
File Size : 54,6 Mb
Release : 1999
Category : Biomathematics
ISBN : 9780821809440

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Differential Equations with Applications to Biology by Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu Pdf

This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas. The 41 papers included in this volume represent the recent work of leading researchers over a wide range of subjects, including bifurcation theory, chaos, stability theory, boundary value problems, persistence theory, neural networks, disease transmission, population dynamics, pattern formation and more. The text would be suitable for a graduate or advanced undergraduate course study in mathematical biology. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.

Introductory Biophysics

James R. Claycomb,Jonathan Tran
Introductory Biophysics Book PDF

Author : James R. Claycomb,Jonathan Tran
Publisher : Jones & Bartlett Learning
Page : 375 pages
File Size : 41,9 Mb
Release : 2011
Category : Medical
ISBN : 9780763779986

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Introductory Biophysics by James R. Claycomb,Jonathan Tran Pdf

Designed for biology, physics, and medical students, Introductory Biophysics: Perspectives on the Living State, provides a comprehensive overview of the complex subject of biological physics. The companion CD-ROM, with MATLAB examples and the student version of QuickFieldTM, allows the student to perform biophysical simulations and modify the textbook example files. Included in the text are computer simulations of thermodynamics, astrobiology, the response of living cells to external fields, chaos in population dynamics, numerical models of evolution, electrical circuit models of cell suspension, gap junctions, and neuronal action potentials. With this text students will be able to perform biophysical simulations within hours. MATLAB examples include; the Hodgkin Huxley equations; the FitzHugh-Nagumo model of action potentials; fractal structures in biology; chaos in population dynamics; the cellular automaton model (the game of life); pattern formation in reaction-diffusion systems. QuickFieldTM tutorials and examples include; calculation of currents in biological tissue; cells under electrical stimulation; induced membrane potentials; heat transfer and analysis of stress in biomaterials.

Fractional Partial Differential Equations and Their Numerical Solutions

Boling Guo,Xueke Pu,Fenghui Huang
Fractional Partial Differential Equations and Their Numerical Solutions Book PDF

Author : Boling Guo,Xueke Pu,Fenghui Huang
Publisher : World Scientific
Page : 348 pages
File Size : 45,7 Mb
Release : 2015-03-09
Category : Mathematics
ISBN : 9789814667067

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Fractional Partial Differential Equations and Their Numerical Solutions by Boling Guo,Xueke Pu,Fenghui Huang Pdf

This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope. This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear Schrödinger equations, fractional Landau–Lifshitz equations and fractional Ginzburg–Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs. Contents:Physics BackgroundFractional Calculus and Fractional Differential EquationsFractional Partial Differential EquationsNumerical Approximations in Fractional CalculusNumerical Methods for the Fractional Ordinary Differential EquationsNumerical Methods for Fractional Partial Differential Equations Readership: Graduate students and researchers in mathematical physics, numerical analysis and computational mathematics. Key Features:This book covers the fundamentals of this field, especially for the beginnersThe book covers new trends and results in this fieldThe book covers numerical results, which will be of broad interests to researchersKeywords:Fractional Partial Differential Equations;Numerical Solutions

Cellular Biophysics and Modeling

Greg Conradi Smith
Cellular Biophysics and Modeling Book PDF

Author : Greg Conradi Smith
Publisher : Cambridge University Press
Page : 395 pages
File Size : 54,9 Mb
Release : 2019-03-14
Category : Mathematics
ISBN : 9781107005365

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Cellular Biophysics and Modeling by Greg Conradi Smith Pdf

What every neuroscientist should know about the mathematical modeling of excitable cells, presented at an introductory level.

Foundations and Tools for Neural Modeling

Jose Mira
Foundations and Tools for Neural Modeling Book PDF

Author : Jose Mira
Publisher : Springer Science & Business Media
Page : 900 pages
File Size : 53,9 Mb
Release : 1999-05-19
Category : Computers
ISBN : 3540660690

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Foundations and Tools for Neural Modeling by Jose Mira Pdf

This book constitutes, together with its compagnion LNCS 1606, the refereed proceedings of the International Work-Conference on Artificial & Neural Networks, IWANN'99, held in Alicante, Spain in June 1999. The 91 revised papers presented were carefully reviewed & selected for inclusion in the book. This volume is devoted to applications of biologically inspired artificial neural networks in various engineering disciplines. The papers are organized in parts on artificial neural nets simulation & implementation, image processing & engineering applications.

Lévy Processes and Stochastic Calculus

David Applebaum
L vy Processes and Stochastic Calculus Book PDF

Author : David Applebaum
Publisher : Cambridge University Press
Page : 461 pages
File Size : 49,6 Mb
Release : 2009-04-30
Category : Mathematics
ISBN : 9781139477987

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Lévy Processes and Stochastic Calculus by David Applebaum Pdf

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Advances in Neural Networks - ISNN 2005

Xiaofeng Liao
Advances in Neural Networks ISNN 2005 Book PDF

Author : Xiaofeng Liao
Publisher : Springer Science & Business Media
Page : 1101 pages
File Size : 42,5 Mb
Release : 2005-05-17
Category : Computers
ISBN : 9783540259121

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Advances in Neural Networks - ISNN 2005 by Xiaofeng Liao Pdf

This book and its sister volumes constitute the proceedings of the 2nd International Symposium on Neural Networks (ISNN 2005). ISNN 2005 was held in the beautiful mountain city Chongqing by the upper Yangtze River in southwestern China during May 30–June 1, 2005, as a sequel of ISNN 2004 successfully held in Dalian, China.

Modeling Life

Alan Garfinkel,Jane Shevtsov,Yina Guo
Modeling Life Book PDF

Author : Alan Garfinkel,Jane Shevtsov,Yina Guo
Publisher : Springer
Page : 445 pages
File Size : 54,8 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9783319597317

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Modeling Life by Alan Garfinkel,Jane Shevtsov,Yina Guo Pdf

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?