Attractors and Methods PDF Download

Author: Boling Guo
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110587262
Category : Mathematics
Languages : en
Pages : 413

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Book Description
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves

Author: Julien C. Sprott
Publisher: M & T Books
ISBN: 9781558512986
Category : Computers
Languages : en
Pages : 426

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Book Description
Chaos and fractals are new mathematical ideas that have revolutionized our view of the world. They have application in virtually every academic discipline. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns. Disk includes a full working version of the program.

Author: Gabrielle Bernstein
Publisher: Hay House, Inc
ISBN: 1401957161
Category : Body, Mind & Spirit
Languages : en
Pages : 249

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Book Description
** NEW YORK TIMES BESTSELLER! ** Ready to take the next step toward living in alignment with the Universe? The #1 New York Times best-selling author of The Universe Has Your Back shows you how. In Super Attractor, Gabrielle Bernstein lays out the essential steps for living in alignment with the Universe--more fully than you've ever done before. "I've always known that there is a nonphysical presence beyond my visible sight," Gabby writes. "All my life I've intuitively tuned in to it and used it as a source for good. . . . What we call it is irrelevant. Connecting to it is imperative." Super Attractor is a manifesto for making that connection and marrying your spiritual life with your day-to-day experience. In these pages, you'll learn to: * Move beyond dabbling in your practice, when it's convenient, to living a spiritual life all the time * Take practical steps to create a life filled with purpose, happiness, and freedom * Feel a sense of awe each day as you witness miracles unfold * Release the past and live without fear of the future * Tap into the infinite source of abundance, joy, and well-being that is your birthright * Bring more light to your own life and the world around you This book is a journey of remembering where your true power lies. You'll learn how to co-create the life you want. You'll accept that life can flow, that attracting is fun, and that you don't have to work so hard to get what you want. Most important, you'll feel good. And when you feel good, you'll give off a presence of joy that can elevate everyone around you. After reading this book, you will know how to fulfill your function: to be a force of love in the world.

Author: Tönu Puu
Publisher: Springer Science & Business Media
ISBN: 9783540402268
Category : Mathematics
Languages : en
Pages : 572

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Book Description
Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.

Author: David N. Cheban
Publisher: World Scientific
ISBN: 9812563083
Category : Mathematics
Languages : en
Pages : 524

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Book Description
The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor.

Author: Tomasz Kapitaniak
Publisher: World Scientific
ISBN: 9814502774
Category : Science
Languages : en
Pages : 101

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Book Description
This book discusses the influence of quasiperiodic force on dynamical system. With this type of forcing, different types of attractors are possible, for example, strange nonchaotic attractors which have some unusual properties.The main part of this book is based on the authors' recent works, but it also presents the results which are the combined achievements of many investigators.

Author: Robert Pryor
Publisher: Routledge
ISBN: 113523129X
Category : Business & Economics
Languages : en
Pages : 255

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Book Description
The Chaos Theory of Careers outlines the application of chaos theory to the field of career development. It draws together and extends the work that the authors have been doing over the last 8 to 10 years. This text represents a new perspective on the nature of career development. It emphasizes the dimensions of careers frequently neglected by contemporary accounts of careers such as the challenges and opportunities of uncertainty, the interconnectedness of current life and the potential for information overload, career wisdom as a response to unplanned change, new approaches to vocational assessment based on emergent thinking, the place of spirituality and the search for meaning and purpose in, with and through work, the integration of being and becoming as dimensions of career development. It will be vital reading for all those working in and studying career development, either at advanced undergraduate or postgraduate level and provides a new and refreshing approach to this fast changing subject. Key themes include: Factors such as complexity, change, and contribution People's aspirations in relation to work and personal fulfilment Contemporary realities of career choice, career development and the working world

Author: Eleonora Bilotta
Publisher: World Scientific
ISBN: 9812790624
Category : Mathematics
Languages : en
Pages : 607

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Book Description
Chaos is considered as one of the most important concepts in modern science. It originally appeared only in computer simulation (the famous Lorenz equation of 1963), but this changed with the introduction of Chua's oscillator (1986) — a simple electronic circuit with the ability to generate a vast range of chaotic behaviors. With Chua's circuit, chaos became a physical phenomenon, readily understood and represented in mathematical language. Yet, even so, it is still difficult for the non-specialist to appreciate the full variety of behaviors that the system can produce.This book aims to bridge the gap. A gallery of nearly 900 “chaotic attractors” — some generated by Chua's physical circuit, the majority through computer simulation of the circuit and its generalizations — are illustrated as 3D color images, time series and fast Fourier transform algorithms. For interested researchers, also presented is the information necessary to replicate the behaviors and images. Finally, how the fractal richness can be plied to artistic ends in generating music and interesting sounds is shown; some examples are included in the DVD-ROM which comes with the book.The contents have also appeared in the International Journal of Bifurcation and Chaos (2007).

Author: Eric Campos Canton
Publisher: World Scientific
ISBN: 9811274134
Category : Science
Languages : en
Pages : 192

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Book Description
What kind of dynamics is a piecewise linear system able to display? How may they generate heteroclinic chaos? How can the coexistence of attractors be designed and characterized? Is it necessary to have equilibrium points to generate chaotic behavior? Chaos theory and complex systems are interesting and evolving topics whose investigation from a theoretical and practical point of view constantly leads to arising questions. Interesting behaviors can be observed in self-excited attractors, hidden attractors and non-self-excited attractors.This book presents some fundamentals of linear system theory and recent approaches to design the three classes of chaotic attractors in piecewise linear systems. Each chapter presents a brief description and basic concepts to provide an overview of linear systems theory; chaos and multistability in integer linear systems; hidden and non-self-excited attractors; and fractional approaches. They also provide example systems to illustrate the concepts and design methods introduced. Some current topics under investigation are addressed from an integer order perspective to make the connection with the fractional order counterpart.This textbook provides a comprehensive introduction, methodologies, and analysis tools to study chaotic piecewise linear systems and will be suitable for undergraduate or graduate students interested in the field of chaos and complex dynamics.

Author: Vladimir V. Chepyzhov
Publisher: American Mathematical Soc.
ISBN: 0821829505
Category : Mathematics
Languages : en
Pages : 377

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Book Description
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For anumber of basic evolution equations of mathematical physics, it was shown that the long time behavior of their solutions can be characterized by a very important notion of a global attractor of the equation. In this book, the authors study new problems related to the theory of infinite-dimensionaldynamical systems that were intensively developed during the last 20 years. They construct the attractors and study their properties for various non-autonomous equations of mathematical physics: the 2D and 3D Navier-Stokes systems, reaction-diffusion systems, dissipative wave equations, the complex Ginzburg-Landau equation, and others. Since, as it is shown, the attractors usually have infinite dimension, the research is focused on the Kolmogorov $\varepsilon$-entropy of attractors. Upperestimates for the $\varepsilon$-entropy of uniform attractors of non-autonomous equations in terms of $\varepsilon$-entropy of time-dependent coefficients are proved. Also, the authors construct attractors for those equations of mathematical physics for which the solution of the corresponding Cauchyproblem is not unique or the uniqueness is not proved. The theory of the trajectory attractors for these equations is developed, which is later used to construct global attractors for equations without uniqueness. The method of trajectory attractors is applied to the study of finite-dimensional approximations of attractors. The perturbation theory for trajectory and global attractors is developed and used in the study of the attractors of equations with terms rapidly oscillating with respect tospatial and time variables. It is shown that the attractors of these equations are contained in a thin neighborhood of the attractor of the averaged equation. The book gives systematic treatment to the theory of attractors of autonomous and non-autonomous evolution equations of mathematical physics.It can be used both by specialists and by those who want to get acquainted with this rapidly growing and important area of mathematics.