Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems
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Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems
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Author : Mariana Haragus
language : en
Publisher:
Release Date : 2011
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems written by Mariana Haragus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Bifurcation theory categories.
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems
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Author : Mariana Haragus
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-23
Local Bifurcations Center Manifolds And Normal Forms In Infinite Dimensional Dynamical Systems written by Mariana Haragus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-23 with Mathematics categories.
An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Patterns Of Dynamics
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Author : Pavel Gurevich
language : en
Publisher: Springer
Release Date : 2018-02-07
Patterns Of Dynamics written by Pavel Gurevich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-07 with Mathematics categories.
Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes.
Applied Mathematics And Scientific Computing
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Author : B. Rushi Kumar
language : en
Publisher: Springer
Release Date : 2019-02-01
Applied Mathematics And Scientific Computing written by B. Rushi Kumar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-01 with Mathematics categories.
This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences (ICAMS), held at the Vellore Institute of Technology in December 2017. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.
Recent Trends In Dynamical Systems
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Author : Andreas Johann
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-24
Recent Trends In Dynamical Systems written by Andreas Johann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Mathematics categories.
This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.
Stochastic Parameterizing Manifolds And Non Markovian Reduced Equations
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Author : Mickaël D. Chekroun
language : en
Publisher: Springer
Release Date : 2014-12-23
Stochastic Parameterizing Manifolds And Non Markovian Reduced Equations written by Mickaël D. Chekroun and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-23 with Mathematics categories.
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Hyperbolic And Kinetic Models For Self Organised Biological Aggregations
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Author : Raluca Eftimie
language : en
Publisher: Springer
Release Date : 2019-01-07
Hyperbolic And Kinetic Models For Self Organised Biological Aggregations written by Raluca Eftimie and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-07 with Mathematics categories.
This book focuses on the spatio-temporal patterns generated by two classes of mathematical models (of hyperbolic and kinetic types) that have been increasingly used in the past several years to describe various biological and ecological communities. Here we combine an overview of various modelling approaches for collective behaviours displayed by individuals/cells/bacteria that interact locally and non-locally, with analytical and numerical mathematical techniques that can be used to investigate the spatio-temporal patterns produced by said individuals/cells/bacteria. Richly illustrated, the book offers a valuable guide for researchers new to the field, and is also suitable as a textbook for senior undergraduate or graduate students in mathematics or related disciplines.
Numerical Bifurcation Analysis For Reaction Diffusion Equations
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Author : Zhen Mei
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Numerical Bifurcation Analysis For Reaction Diffusion Equations written by Zhen Mei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce nario, mode-interactions and impact of boundary conditions.
Pde Dynamics
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Author : Christian Kuehn
language : en
Publisher: SIAM
Release Date : 2019-04-10
Pde Dynamics written by Christian Kuehn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Bifurcation Theory
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Author : Hansjörg Kielhöfer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-13
Bifurcation Theory written by Hansjörg Kielhöfer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-13 with Mathematics categories.
In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.