|
|
|
The Four Cardinal Virtues
|
|
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (Computational Neuroscience)
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..
Price: $42.99
[ Notify me when price goes down.]
|
|
Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics (Academic Press), 60.)
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems. * Provides a rigorous yet accessible introduction to differential equations and advanced mathematics * The revision of this seminal book brings material and presentation up to date * Linear algebra prerequisites have been toned down from the first edition * Includes analyses of examples of chaotic systems, including Lorenz, Rosssler, and Shil'nikov systems * Bifurcation theory included throughout.
Price: $52.50
[ Notify me when price goes down.]
|
|
Complexity Explained (Springer Complexity)
This book explains why complex systems research is important in understanding the structure, function and dynamics of complex natural and social phenomena. It illuminates how complex collective behavior emerges from the parts of a system, due to the interaction between the system and its environment. You will learn the basic concepts and methods of complex system research. It is shown that very different complex phenomena of nature and society can be analyzed and understood by nonlinear dynamics since many systems of very different fields, such as physics, chemistry, biology, economics, psychology and sociology etc. have similar architecture. “Complexity Explained” is not highly technical and mathematical, but teaches and uses the basic mathematical notions of dynamical system theory making the book useful for students of science majors and graduate courses, but it should be readable for a more general audience; actually for those, who ask: What complex systems really are? .
Price: $49.60
[ Notify me when price goes down.]
|
|
Dynamical Systems with Applications using Mathematica®
Dynamical Systems with Applications Using Mathematica® provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Throughout the book, the author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum. The first part of the book deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems. Exercises are included at the end of every chapter. Both textbooks and research papers are presented in the list of references. Working Mathematica notebooks will be available at http://library.wolfram.com/infocenter/Books/AppliedMathematics/. The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. The material is also accessible to readers with a general mathematical background. Many chapters of the book are especially useful as reference material for senior undergraduate independent project work. .
Price: $45.33
[ Notify me when price goes down.]
|
|
A First Course In Chaotic Dynamical Systems: Theory And Experiment (Studies in Nonlinearity)
A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton’s method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented. Chaotic Dynamical Systems Software, Labs 1–6 is a supplementary laboratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems, it leads to a rich understanding of this emerging field. .
Price: $29.94
[ Notify me when price goes down.]
|
|
Chaos
CHAOS: An Introduction to Dynamical Systems was developed and class-tested by a distinguished team of authors at two universities through their teaching of courses based on the material. Intended for courses in nonlinear dynamics offered either in Mathematics or Physics, the text requires only calculus, differential equations, and linear algebra as prerequisites. Spanning the wide reach of nonlinear dynamics throughout mathematics, natural and physical science, CHAOS develops and explains the most intriguing and fundamental elements of the topic and examines their broad implications. Among the major topics included are: discrete dynamical systems, chaos, fractals, nonlinear differential equations, and bifurcations. The text also features Lab Visits, short reports that illustrate relevant concepts from the physical, chemical, and biological sciences, drawn from the scientific literature. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulation, designed to be used with any software package. And each chapter ends with a Challenge, which provides students a tour through an advanced topic in the form of an extended exercise..
Price: $44.14
[ Notify me when price goes down.]
|
|
|
|
|