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Ordinary Differential Equations
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by
Vladimir I Arnol'd
There are dozens of books on ODEs, but none with the elegant geometric insight of Arnol'd's book. Arnol'd puts a clear emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on theroutine presentation of algorithms for solving special classes of equations.Of course, the reader learns how to solve equations, ...
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Dynamics and Bifurcations
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by
Jack K Hale
The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications ...
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Mathematics for Dynamic Modeling
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Edward Beltrami
This new edition of "Mathematics for Dynamic Modeling" updates a widely used and highly-respected textbook. The text is appropriate for upper-level undergraduate and graduate level courses in modeling, dynamical systems, differential equations, and linear multivariable systems offered in a variety of departments including mathematics, engineering, ...
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Differential Equations and Dynamical Systems
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by
Lawrence Perko
This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material ...
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A First Course in Chaotic Dynamical Systems: Theory and Experiment
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by
Robert L Devaney
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 ...
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Introduction to Applied Nonlinear Dynamical Systems and Chaos
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by
Stephen Wiggins, A Heck, Stephen Wiggens
This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. ...
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A First Course in Discrete Dynamical Systems
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Richard A Holmgren
Discrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The ...
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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John Guckenheimer, Philip Holmes (Photographer), F John (Editor)
From the reviews: 'This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from ...
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Chaos: An Introduction to Dynamical Systems
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Kathleen Alligood (Editor), Timothy Sauer, James A Yorke
"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, this text requires only calculus, differential equations, and linear ...
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Discrete Chaos: With Applications in Science and Engineering
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by
Saber N Elaydi
This edition now includes recent results on global stability, bifurcation, chaos, and fractals. It covers trace-determinant stability, bifurcation analysis, the center manifold theory, L-systems, and the Mandelbrot set as well as applications in biology, chemistry, and physics. The book also offers PHASER software on a CD-ROM and Maple and ...
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A visual introduction to dynamical systems theory for psychology
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Frederick David Abraham, Ralph Abraham, Christopher D. Shaw
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Nonlinear Differential Equations and Dynamical Systems
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by
Ferdinand Verhulst
A good book for a nice price!
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Instabilities and Fronts in Extended Systems
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by
Pierre Collet, Jean-Pierre Eckmann
The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of these objects are discussed. To the uninitiated reader, the theoretical methods that lead to the various results ...
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On the Geometry of Diffusion Operators and Stochastic Flows
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by
K D Elworthy, D Elworthy, Y Le Jan
Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path ...
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Stochastic Dynamics
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by
Hans Crauel (Editor), Matthias Gundlach (Editor)
This volume gives an account of new and recent developments in the theory of random and, in particular, stochastic dynamical systems. Its purpose is to document and, to some extent, summarise the current state of the field of random dynamical systems beyond the recent monograph, "Random Dynamical Systems" by Ludwig Arnold. The book is intended for ...
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Averaging Methods in Nonlinear Dynamical Systems
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by
Jan A Sanders, Ferdinand Verhulst
Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the "Averaging Methods in Nonlinear Dynamical Systems" book. There are many changes, corrections and updates in chapters on Basic Material ...
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Flavors of Geometry
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Silvio Levy (Editor)
Flavors of Geometry is a volume of lectures on four geometrically-influenced fields of mathematics that have experienced great development in recent years. Growing out of a series of introductory lectures given at the Mathematical Sciences Research Institute in January 1995 and January 1996, the book presents chapters by masters in their ...
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Normal Forms and Unfoldings for Local Dynamical Systems
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by
James Murdock
The largest part of this book is devoted to normal forms, divided into semisimple theory, applied when the linear part is diagonalizable, and the general theory, applied when the linear part is the sum of the semisimple and nilpotent matrices. One of the objectives of this book is to develop all of the necessary theory 'from scratch' in just the ...
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Tangency, Flow Invariance for Differential Equations, and Optimization Problems
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by
Dumitru Motreanu, Nicolae H Pavel, Pavel H Pavel
Provides a great deal of material that is completely new to the field of flow invariance, offering fresh insights for experienced mathematicians and rigorous training for students new to the specialty. Four useful appendices supply the methods used throughout the book, making it a totally self-referential and self-contained unit. Features many ...
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Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting
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by
Eugene M Izhikevich
This book 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 ...
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Autoparametric Resonance in Mechanical Systems
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Ales Tondl, M Ruijgrok, Thijs Ruijgrok
When a mechanical system has two or more coupled vibrating components, the vibration of one of the components may destabilize the motion of the others. This destabilization effect, autoparametric resonance, is a concept that has important engineering applications. This book is the first completely devoted to the subject of autoparametric resonance ...
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A First Course in Dynamics: With a Panorama of Recent Developments
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by
Boris Hassleblatt, Anatole Katok
The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate ...
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Chaotic Transport in Dynamical Systems
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by
Stephen Wiggins
Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time ...
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Discrete Dynamical Systems: Theory and Applications
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by
James T Sandefur
This textbook is an elementary introduction to the world of dynamical systems and chaos. Dynamical systems provide a mathematical means of modelling and analyzing aspects of the changing world around us. The aim of this text is to introduce the reader both to the wide variety of techniques used to study dynamical systems and to their many ...
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An Introduction to Symbolic Dynamics and Coding
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by
Douglas Lind, Brian Marcus
Symbolic dynamics is a rapidly growing area of dynamical systems. Although it originated as a method to study general dynamical systems, it has found significant uses in coding for data storage and transmission as well as in linear algebra. This book is the first general textbook on symbolic dynamics and its applications to coding. It will serve ...
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