Continuous and Discrete Dynamics Near Manifolds of Equilibria
Author: B. Aulbach
Publisher:
Published: 2014-01-15
Total Pages: 156
ISBN-13: 9783662161401
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Continuous and discrete dynamics near manifolds of equilibria
Author: Bernd Aulbach
Publisher:
Published: 1983
Total Pages: 136
ISBN-13:
DOWNLOAD EBOOKContinuous and Discrete Dynamics near Manifolds of Equilibria
Author: B. Aulbach
Publisher: Springer
Published: 2006-11-14
Total Pages: 150
ISBN-13: 3540388532
DOWNLOAD EBOOKEntfesseln 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
Geometric Theory of Discrete Nonautonomous Dynamical Systems
Author: Christian Pötzsche
Publisher: Springer Science & Business Media
Published: 2010-09-17
Total Pages: 422
ISBN-13: 3642142575
DOWNLOAD EBOOKThe goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Theory of Translation Closedness for Time Scales
Author: Chao Wang
Publisher: Springer Nature
Published: 2020-05-05
Total Pages: 586
ISBN-13: 3030386449
DOWNLOAD EBOOKThis 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.
Combined Measure and Shift Invariance Theory of Time Scales and Applications
Author: Chao Wang
Publisher: Springer Nature
Published: 2022-09-22
Total Pages: 443
ISBN-13: 3031116194
DOWNLOAD EBOOKThis 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.
Dynamic Equations on Time Scales
Author: Martin Bohner
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 365
ISBN-13: 1461202019
DOWNLOAD EBOOKOn becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.
Probability and Partial Differential Equations in Modern Applied Mathematics
Author: Edward C. Waymire
Publisher: Springer Science & Business Media
Published: 2010-06-14
Total Pages: 265
ISBN-13: 038729371X
DOWNLOAD EBOOK"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.
Dynamic Systems on Measure Chains
Author: V. Lakshmikantham
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 300
ISBN-13: 1475724497
DOWNLOAD EBOOKFrom 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.
Singularities and Groups in Bifurcation Theory
Author: Martin Golubitsky
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 551
ISBN-13: 1461245745
DOWNLOAD EBOOKBifurcation 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.
