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Continuous And Discrete Dynamics Near Manifolds Of Equilibria
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Book Synopsis Continuous and Discrete Dynamics Near Manifolds of Equilibria by : B. Aulbach
Download or read book Continuous and Discrete Dynamics Near Manifolds of Equilibria written by B. Aulbach and published by . This book was released on 2014-01-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Continuous and discrete dynamics near manifolds of equilibria by : Bernd Aulbach
Download or read book Continuous and discrete dynamics near manifolds of equilibria written by Bernd Aulbach and published by . This book was released on 1983 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Continuous and Discrete Dynamics near Manifolds of Equilibria by : B. Aulbach
Download or read book Continuous and Discrete Dynamics near Manifolds of Equilibria written by B. Aulbach and published by Springer. This book was released on 2006-11-14 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entfesseln Sie die Kreativität Ihres Kindes mit über 35 einzigartigen Seite zum Färben! Sie werden viele beliebte Dinosaurier-Typen hier zu finden. Dieses Buch ist eine erstaunliche Aktivität, um die Phantasie und Kreativität Ihres Kindes zu stimulieren. Dieses tolle Buch wird Ihrem Kind auch den Namen einiger Dinosaurier beibringen, während Sie Spaß beim Färben haben. Ein perfektes Geschenk für Dinosaurier-Fans! Jede Ausmalseite ist auf einer separaten Seite gedruckt, um ein Durchbluten zu vermeiden. Geeignet für Marker, Buntstifte, Wasserfarbe, Gelstifte. Große Größe - 8,5 x 11 Zoll
Book Synopsis Theory of Translation Closedness for Time Scales by : Chao Wang
Download or read book Theory of Translation Closedness for Time Scales written by Chao Wang and published by Springer Nature. This book was released on 2020-05-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.
Book Synopsis Combined Measure and Shift Invariance Theory of Time Scales and Applications by : Chao Wang
Download or read book Combined Measure and Shift Invariance Theory of Time Scales and Applications written by Chao Wang and published by Springer Nature. This book was released on 2022-09-22 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.
Book Synopsis Probability and Partial Differential Equations in Modern Applied Mathematics by : Edward C. Waymire
Download or read book Probability and Partial Differential Equations in Modern Applied Mathematics written by Edward C. Waymire and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.
Book Synopsis Dynamic Systems on Measure Chains by : V. Lakshmikantham
Download or read book Dynamic Systems on Measure Chains written by V. Lakshmikantham and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a modelling point of view, it is more realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time as an arbitrary closed set of reals called time-scale or measure chain. It is therefore natural to ask whether it is possible to provide a framework which permits us to handle both dynamic systems simultaneously so that one can get some insight and a better understanding of the subtle differences of these two different systems. The answer is affirmative, and recently developed theory of dynamic systems on time scales offers the desired unified approach. In this monograph, we present the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on time scales. In chapter two, we introduce dynamic systems on time scales and prove the basic properties of solutions of such dynamic systems. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. Some important features of the monograph are as follows: It is the first book that is dedicated to a systematic development of the theory of dynamic systems on time scales which is of recent origin. It demonstrates the interplay of the two different theories, namely, the theory of continuous and discrete dynamic systems, when imbedded in one unified framework. It provides an impetus to investigate in the setup of time scales other important problems which might offer a better understanding of the intricacies of a unified study.£/LIST£ Audience: The readership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets.
Book Synopsis Singularities and Groups in Bifurcation Theory by : Martin Golubitsky
Download or read book Singularities and Groups in Bifurcation Theory written by Martin Golubitsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.
Book Synopsis Global Analysis of Dynamical Systems by : H.W Broer
Download or read book Global Analysis of Dynamical Systems written by H.W Broer and published by CRC Press. This book was released on 2001-06-18 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.
Book Synopsis Shadowing in Dynamical Systems by : K.J. Palmer
Download or read book Shadowing in Dynamical Systems written by K.J. Palmer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.
Book Synopsis Analysis and Optimization of Differential Systems by : Viorel Barbu
Download or read book Analysis and Optimization of Differential Systems written by Viorel Barbu and published by Springer. This book was released on 2013-06-05 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations; Control theory of Partial Differential Equations (PDE's); Optimization methods in PDE's with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems. These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering. This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.
Book Synopsis Six Lectures on Dynamical Systems by : Bernd Aulbach
Download or read book Six Lectures on Dynamical Systems written by Bernd Aulbach and published by World Scientific. This book was released on 1996 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included.The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level.
Book Synopsis Ordinary and Partial Differential Equations by : Brian D. Sleeman
Download or read book Ordinary and Partial Differential Equations written by Brian D. Sleeman and published by Springer. This book was released on 2006-11-14 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Dynamical Systems by : B. Fiedler
Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Around Classification Theory of Models by : Saharon Shelah
Download or read book Around Classification Theory of Models written by Saharon Shelah and published by Springer. This book was released on 2006-12-08 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamical Systems and Cosmology by : A.A. Coley
Download or read book Dynamical Systems and Cosmology written by A.A. Coley and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary differential equations. In this book we discuss cosmological models as dynamical systems, with particular emphasis on applications in the early Universe. We point out the important role of self-similar models. We review the asymptotic properties of spatially homogeneous perfect fluid models in general relativity. We then discuss results concerning scalar field models with an exponential potential (both with and without barotropic matter). Finally, we discuss the dynamical properties of cosmological models derived from the string effective action. This book is a valuable source for all graduate students and professional astronomers who are interested in modern developments in cosmology.
Book Synopsis Dynamics and Bifurcations by : Jack K. Hale
Download or read book Dynamics and Bifurcations written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.