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| Author | : William A. Brock |
| Publisher | : MIT Press |
| Total Pages | : 362 |
| Release | : 1991 |
| Genre | : Business & Economics |
| ISBN | : 9780262023290 |
Brock, Hsieh, and LeBaron show how the principles of chaos theory can be applied to such areas of economics and finance as the changing structure of stock returns and nonlinearity in foreign exchange.
| Author | : Paul Glendinning |
| Publisher | : Cambridge University Press |
| Total Pages | : 408 |
| Release | : 1994-11-25 |
| Genre | : Mathematics |
| ISBN | : 9780521425667 |
An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.
| Author | : Paul Manneville |
| Publisher | : World Scientific |
| Total Pages | : 416 |
| Release | : 2004 |
| Genre | : Science |
| ISBN | : 9781860944833 |
This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and potentially to anyone who wants to learn about recent advances in the field of applied nonlinear dynamics. Technicalities are, however, not completely avoided. They are instead explained as simply as possible using heuristic arguments and specific worked examples.
| Author | : Michail Zak |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 559 |
| Release | : 2008-12-11 |
| Genre | : Science |
| ISBN | : 3540691219 |
So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi bility in thermodynamics, the phenomena of chaos and turbulence in clas sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.
| Author | : Steven H. Strogatz |
| Publisher | : CRC Press |
| Total Pages | : 532 |
| Release | : 2018-05-04 |
| Genre | : Mathematics |
| ISBN | : 0429961111 |
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
| Author | : Thierry Vialar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 752 |
| Release | : 2009-04-26 |
| Genre | : Business & Economics |
| ISBN | : 3540859780 |
Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book.
| Author | : F.Tito Arecchi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 260 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 364271708X |
Of the variety of nonlinear dynamical systems that exhibit deterministic chaos optical systems both lasers and passive devices provide nearly ideal systems for quantitative investigation due to their simplicity both in construction and in the mathematics that describes them. In view of their growing technical application the understanding, control and possible exploitation of sources of instability in these systems has considerable practical importance. The aim of this volume is to provide a comprehensive coverage of the current understanding of optical instabilities through a series of reviews by leading researchers in the field. The book comprises nine chapters, five on active (laser) systems and four on passive optically bistable systems. Instabilities and chaos in single- (and multi-) mode lasers with homogeneously and broadened gain media are presented and the influence of an injected signal, loss modulation and also feedback of laser output on this behaviour is treated. Both electrically excited and optically pumped gas lasers are considered, and an analysis of dynamical instabilities in the emission from free electron lasers are presented. Instabilities in passive optically bistable systems include a detailed analysis of the global bifurcations and chaos in which transverse effects are accounted for. Experimental verification of degenerative pulsations and chaos in intrinsic bistable systems is described for various optical feedback systems in which atomic and molecular gases and semiconductors are used as the nonlinear media. Results for a hybrid bistable optical system are significant in providing an important test of current understanding of the dynamical behaviour of passive bistable systems.
| Author | : Albert C. J. Luo |
| Publisher | : Springer |
| Total Pages | : 213 |
| Release | : 2018-01-16 |
| Genre | : Technology & Engineering |
| ISBN | : 9811052425 |
This book provides students and researchers with a systematic solution for fluid-induced structural vibrations, galloping instability and the chaos of cables. They will also gain a better understanding of stable and unstable periodic motions and chaos in fluid-induced structural vibrations. Further, the results presented here will help engineers effectively design and analyze fluid-induced vibrations.
| Author | : William A. Barnett |
| Publisher | : Cambridge University Press |
| Total Pages | : 426 |
| Release | : 1996-10-28 |
| Genre | : Business & Economics |
| ISBN | : 9780521471411 |
This 1997 book presents developments in nonlinear economic dynamics along with related research from other fields, including mathematics, statistics, biology, and physics.
| Author | : Junji Ohtsubo |
| Publisher | : Springer |
| Total Pages | : 679 |
| Release | : 2017-05-03 |
| Genre | : Science |
| ISBN | : 3319561383 |
This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in semiconductor lasers are discussed, but also for example the method of self-mixing interferometry in quantum-cascade lasers, which is indispensable in practical applications. Further, this edition covers chaos synchronization between two lasers and the application to secure optical communications. Another new topic is the consistency and synchronization property of many coupled semiconductor lasers in connection with the analogy of the dynamics between synaptic neurons and chaotic semiconductor lasers, which are compatible nonlinear dynamic elements. In particular, zero-lag synchronization between distant neurons plays a crucial role for information processing in the brain. Lastly, the book presents an application of the consistency and synchronization property in chaotic semiconductor lasers, namely a type of neuro-inspired information processing referred to as reservoir computing.
