Dynamics of Nonlinear Waves in Dissipative Systems Reduction, Bifurcation and Stability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dynamics of Nonlinear Waves in Dissipative Systems Reduction, Bifurcation and Stability write by G Dangelmayr. This book was released on 1996-08-01. Dynamics of Nonlinear Waves in Dissipative Systems Reduction, Bifurcation and Stability available in PDF, EPUB and Kindle. The mathematical description of complex spatiotemporal behaviour observed in dissipative continuous systems is a major challenge for modern research in applied mathematics. While the behaviour of low-dimensional systems, governed by the dynamics of a finite number of modes is well understood, systems with large or unbounded spatial domains show intrinsic infinite-dimensional behaviour --not a priori accessible to the methods of finite dimensionaldynamical systems. The purpose of the four contributions in this book is to present some recent and active lines of research in evolution equations posed in large or unbounded domains. One of the most prominent features of these systems is the propagation of various types of patterns in the form of waves, such as travelling and standing waves and pulses and fronts. Different approaches to studying these kinds of phenomena are discussed in the book. A major theme is the reduction of an original evolution equation in the form of a partial differential equation system to a simpler system of equations, either a system of ordinary differential equation or a canonical system of PDEs. The study of the reduced equations provides insight into the bifurcations from simple to more complicated solutions and their stabilities. .
Handbook of Dynamical Systems
Handbook of Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of Dynamical Systems write by B. Fiedler. This book was released on 2002-02-21. Handbook of Dynamical Systems available in PDF, EPUB and Kindle. This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.
Radially Symmetric Patterns of Reaction-Diffusion Systems
Radially Symmetric Patterns of Reaction-Diffusion Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Radially Symmetric Patterns of Reaction-Diffusion Systems write by Arnd Scheel. This book was released on 2003. Radially Symmetric Patterns of Reaction-Diffusion Systems available in PDF, EPUB and Kindle. Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.
Mathematics of Complexity and Dynamical Systems
Mathematics of Complexity and Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematics of Complexity and Dynamical Systems write by Robert A. Meyers. This book was released on 2011-10-05. Mathematics of Complexity and Dynamical Systems available in PDF, EPUB and Kindle. Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Trends in Nonlinear Analysis
Trends in Nonlinear Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Trends in Nonlinear Analysis write by Markus Kirkilionis. This book was released on 2013-04-17. Trends in Nonlinear Analysis available in PDF, EPUB and Kindle. Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.
