Download or read book The Structure of Attractors in Dynamical Systems written by N.G. Markley and published by Springer. This book was released on 2007-01-05 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Structure of Attractors in Dynamical Systems written by N. G. Markley and published by . This book was released on 2014-01-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Structure of Attractors in Dynamical Systems written by Nelson Groh Markley and published by . This book was released on 1978 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Structure of Attractors in Dynamical Systems written by John Calhoun Martin and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Attractors and Methods written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-09 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Global Attractors of Non autonomous Dissipative Dynamical Systems written by David N. Cheban and published by World Scientific. This book was released on 2004 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dynamical Systems IX written by D.V. Anosov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details).
Download or read book Global Attractors Of Non autonomous Dynamical And Control Systems 2nd Edition written by Cheban David N and published by World Scientific. This book was released on 2014-12-15 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations.The new Chapters 15-17 added to this edition include some results concerning Control Dynamical Systems — the global attractors, asymptotic stability of switched systems, absolute asymptotic stability of differential/difference equations and inclusions — published in the works of author in recent years.
Download or read book Infinite Dimensional Dynamical Systems written by James C. Robinson and published by Cambridge University Press. This book was released on 2001-04-23 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.
Download or read book Attractors Under Discretisation written by Xiaoying Han and published by Springer. This book was released on 2017-08-11 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
Download or read book Neural Fields written by Stephen Coombes and published by Springer. This book was released on 2014-06-17 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.
Download or read book Global Attractors Of Nonautonomous Dissipative Dynamical Systems written by David N Cheban and published by World Scientific. This book was released on 2004-11-29 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations. Intended for experts in qualitative theory of differential equations, dynamical systems and their applications, this accessible book can also serve as an important resource for senior students and lecturers.
Download or read book On the characterization and robustness of the attractors of multivalued dynamical systems written by Rubén Caballero Toro and published by Universidad Miguel Hernández. This book was released on with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: El objetivo de este trabajo es estudiar sistemas dinámicos multivaluados. En particular, pretendemos obtener resultados relacionados con la estructura de los atractores para describir el comportamiento de las soluciones de diferentes ecuaciones. Por tanto, nuestra investigación puede situarse en el área de Matemática Aplicada. Más concretamente, el Capítulo 1 versa sobre la robustez de los semiflujos multivaluados dinámicamente gradientes. Para aplicar este resultado describimos las propiedades dinámicas de una familia de problemas Chafee-Infante aproximando una inclusión diferencial, demostrando que las soluciones débiles de estos problemas generan un semiflujo multivaluado dinámicamente gradiente con respecto a unos conjuntos de Morse. El Capítulo 2 se centra en una ecuación más general llamada ecuación de reacción-difusión no local, donde el término de difusión depende del gradiente de la solución. En primer lugar, demostramos la existencia y unicidad de soluciones regulares y fuertes. En segundo lugar, obtenemos la existencia de atractores globales en ambas situaciones bajo supuestos bastante débiles al definir un semiflujo multivaluado. En el último capítulo estudiamos la estructura del atractor global para el semiflujo multivaluado generado por una ecuación de reacción-difusión no local donde no podemos garantizar la unicidad del problema de Cauchy. Comenzamos analizando la existencia y propiedades de los puntos estacionarios, mostrando que el problema sufre la misma cascada de bifurcaciones que en la ecuación de Chafee-Infante. Para concluir, estudiamos la estabilidad de los puntos fijos y establecemos que el semiflujo es dinámicamente gradiente. Además, probamos que el atractor está formado por los puntos estacionarios y sus conexiones heteroclínicas y analizamos algunas de las posibles conexiones.
Download or read book Nonautonomous Dynamical Systems written by Peter E. Kloeden and published by American Mathematical Soc.. This book was released on 2011-08-17 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.
Download or read book Attractors and Inertial Manifolds written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-09 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
Download or read book Frontiers in the Study of Chaotic Dynamical Systems with Open Problems written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2011-03-08 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field. Contents:Problems with Lorenz's Modeling and the Algorithm of Chaos Doctrine (S OuYang & Y Lin)Nonexistence of Chaotic Solutions of Nonlinear Differential Equations (L S Yao)Some Open Problems in the Dynamics of Quadratic and Higher Degree Polynomial ODE Systems (F Zhang & J Heidel)On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems (G M Mahmoud)On the Study of Chaotic Systems with Non-Horseshoe Template (A Ray et al.)Instability of Solutions of Fourth and Fifth Order Delay Differential Equations (C Tunç)Some Conjectures About the Synchronizability and the Topology of Networks (A Caneco et al.)Wavelet Study of Dynamical Systems Using Partial Differential Equations (E B Postnikov)Combining the Dynamics of Discrete Dynamical Systems (J S Cánovas)Code Structure for Pairs of Linear Maps with Some Open Problems (P Troshin)Recent Advances in Open Billiards with Some Open Problems (C P Dettmann)Open Problems in the Dynamics of the Expression of Gene Interaction Networks (L S Liebovitch & V Naudot)How to Transform a Type of Chaos in Dynamical Systems? (E Zeraoulia & J C Sprott) Readership: Graduate students and researchers interested in chaotic dynamical systems. Keywords:Nonlinear Differential Equations;Lorenz Modeling;ODE;Discrete Dynamical Systems;Chaotic Systems
Download or read book Analysis and Control of Complex Dynamical Systems written by Kazuyuki Aihara and published by Springer. This book was released on 2015-03-20 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.
