Books about Bifurcation from Amazon.com

This book applied the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking the cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help the reader develop an intuitive feel for the properties involved. In this fifth printing the authors have corrected further errors, oversights and updates..
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This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first edition, while updating the context to incorporate recent theoretical developments, in particular, new and improved numerical methods for bifurcation analysis. Reviews of the first edition:.
Price: $69.26 [Notify me when price goes down.]

This book of ideas and examples about the geometry of dynamics and bifurcations of ordinary differential equations The subject of differential and difference equations is an old and much-honored chapter in science. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications. It is the aim of this book to provide a modest foundation of knowledge for undergraduate and beginning graduate students in mathematics or science and engineering. Equations in dimension one and two constitute the majority of the text. It is demonstrated in particular that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Proceeding, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits, appear..
Price: $28.21 [Notify me when price goes down.]

This well-known booklet, now in its third, expanded edition, provides an informal survey of applications of singularity theory in a wide range of areas. Although the first few chapters touch briefly (and critically) on theThom-Zeeman catastrophe theory, most of the book is concerned with more recent and less controversial aspects, covering such topics as: bifurcations and stability loss, wavefront propagation, the distribution of matter in the universe, optimization and control problems, visible contours,bypassing an obstacle, symplectic and contact geometry, complex singularities, and the surprising connections between singularities and widely disparate mathematical objects such as regular polyhedra and reflection groups. Readers familiar with the previous editions will find much that is new. Results have been brought up to date, and among the new or expanded topics discussed are delayed loss of stability, cascades of period doublings and triplings, shock waves, implicit differential equationsand folded singularities, interior scattering, and more. Three new sections give an overview of the history of singularity theory and its applications from Leonardo da Vinci to modern times, a discussion of perestroika in terms of the theory of metamorphoses, and a list of 93 problems touching on most of the subject matter in the book. The text is enhanced by fifteen new drawings (there are now 87 in all) and improvements to old ones. The already extensive literature list has been updated and expanded. As a result, the book has been enlarged by almost a third. Arnol'd's goal with this edition remains the same: to explain the essence of the results and applications to readers having a minimal mathematical background. All that he asks, is that the reader have an inquiring mind..
Price: $24.99 [Notify me when price goes down.]

This book is the first systematic presentation of the theory of dynamical systems under the influence of randomness It includes products of random mappings as well as random and stochastic differential equations. The basic mulitplicative ergodic theorem is presented and provides a random substitute for linear algebra. On its basis random invariant manifolds are constructed, systems are simplified by smooth random coordinate transformations (random normal forms), and qualitative changes in families of random systems (random bifurcation theory) are studied. Numerous instructive examples are treated analytically or numerically. The main intention, however, is to present a reliable and rather complete source of reference which lays the foundation for future work and applications..
Price: $104.30 [Notify me when price goes down.]

The interaction between mathematics and mechanics is a never ending source of new developments. This present textbook includes a wide –ranging spectrum of topics from the three body problem and gyroscope theory to bifurcation theory, optimization, control and continuum mechanics of elastic bodies and fluids. For each of the covered topics the reader can practice mathematical experiments by using a large assortment of Matlab-programs which are available on the author’s homepage. The self-contained and clear presentation including Matlab is often useful to teach technical details by the program itself (learning by doing), which was not possible by just presenting the formula in the past. The reader will be able to produce each picture or diagram from the book by themselves and to arbitrarily alter the data or algorithms.

Recent Review of the German edition

"This book introduces the engineering-oriented reader to all the mathematical tools necessary for solving complex problems in the field of mechanics. The mathematics- oriented reader will find various applications of mathematical and numerical methods for modelling comprehensive mechanical-technical practical problems. Therefore this book will be interesting not only for students of various fields but also for practitioners, development engineers or mathematicians" (Hans Bufler, in: Zentralblatt MATH, 2007, Vol. 1100, Issue 2)

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Price: $71.96 [Notify me when price goes down.]

The book deals with parameter dependent problems of the form u"+*f(u)=0 on an interval with homogeneous Dirichlet or Neuman boundary conditions. These problems have a family of solution curves in the (u,*)-space. By examining the so-called time maps of the problem the shape of these curves is obtained which in turn leads to information about the number of solutions, the dimension of their unstable manifolds (regarded as stationary solutions of the corresponding parabolic prob- lem) as well as possible orbit connections between them. The methods used also yield results for the period map of certain Hamiltonian systems in the plane. The book will be of interest to researchers working in ordinary differential equations, partial differential equations and various fields of applications. By virtue of the elementary nature of the analytical tools used it can also be used as a text for undergraduate and graduate students with a good background in the theory of ordinary differential equations..
Price: $20.65 [Notify me when price goes down.]

Traditional analysis of dynamical systems has restricted its attention to smooth problems, but it has become increasingly clear that there are distinctive phenomena unique to discontinuous systems that can be analyzed mathematically but which fall outside the usual methodology for smooth dynamical systems.

The primary purpose of this book is to present a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction asserts the ubiquity of such models with examples drawn from mechanics, electronics, control theory and physiology. The main thrust is to classify complex behavior via bifurcation theory in a systematic yet applicable way. The key concept is that of a discontinuity-induced bifurcation, which generalizes diverse phenomena such as grazing, border-collision, sliding, chattering and the period-adding route to chaos. The results are presented in an informal style and illustrated with copious examples, both theoretical and experimental.

Aimed at a wide audience of applied mathematicians, engineers and scientists at the early postgraduate level, the book assumes only the standard background of basic calculus and linear algebra for most of the presentation and will be an indispensable resource for students and researchers. The inclusion of a comprehensive bibliography and many open questions will also serve as a stimulus for future research.

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Price: $73.19 [Notify me when price goes down.]

For more than a hundred years, dissociative states, sometimes referred to as multiple personality disorder, have fascinated the public as well as scientists. The precise nature of this disorder is a controversial one, dividing clinicians, theorists, and researchers. Challenging the conventional wisdom on all sides, Robert Rieber’s Bifurcation of the Self traces the clinical and social history of dissociation in a provocative examination of this widely debated phenomenon.

At the core of this history is a trio of related evolutions—hypnosis, concepts of identity, and dissociation—beginning with nineteenth-century "hysterics" and culminating in the modern boom in Dissociative Identity Disorder (DID) diagnoses and the parallel rise in childhood abuse/repressed memory cases. Rieber does not argue the non-existence of DID; rather he asserts that it is a rare disorder exaggerated by dissociation advocates and exploited by the media. In doing so, he takes on some of the most difficult questions in the field:

- How crucial is memory to a person’s identity?

- Can two or more autonomous personalities actually exist in the same body?

- If trauma causes dissociation, why aren’t there more DID cases?

- Why are DID cases prevalent in some eras but not in others?

- Does dissociative disorder belong in the DSM?

The book is rigorously illustrated with two centuries’ worth of famous cases including Christine Beauchamp, Ansel Bourne, Eve Black/Eve White, and most notably the woman known as "Sybil", whose story is covered in depth with newly revealed manuscripts. And Rieber reviews the current state of DID-related controversy, from the professionals who feel that the condition is underreported to those who consider it a form of malingering, so that readers may draw their own conclusions.

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Price: $53.25 [Notify me when price goes down.]