Monotone Nonautonomous Dynamical Systems
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Monotone Nonautonomous Dynamical Systems
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Author : David N. Cheban
language : en
Publisher: Springer Nature
Release Date : 2024-07-15
Monotone Nonautonomous Dynamical Systems written by David N. Cheban and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-15 with Mathematics categories.
The monograph present ideas and methods, developed by the author, to solve the problem of existence of Bohr/Levitan almost periodic (respectively, almost recurrent in the sense of Bebutov, almost authomorphic, Poisson stable) solutions and global attractors of monotone nonautonomous differential/difference equations. Namely, the text provides answers to the following problems: 1. Problem of existence of at least one Bohr/Levitan almost periodic solution for cooperative almost periodic differential/difference equations; 2. Problem of existence of at least one Bohr/Levitan almost periodic solution for uniformly stable and dissipative monotone differential equations (I. U. Bronshtein’s conjecture, 1975); 3. Problem of description of the structure of the global attractor for monotone nonautonomous dynamical systems; 4. The structure of the invariant/minimal sets and global attractors for one-dimensional monotone nonautonomous dynamical systems; 5. Asymptotic behavior of monotone nonautonomous dynamical systems with a first integral (Poisson stable motions, convergence, asymptotically Poisson stable motions and structure of the Levinson center (compact global attractor) of dissipative systems); 6. Existence and convergence to Poisson stable motions of monotone sub-linear nonautonomous dynamical systems. This book will be interesting to the mathematical community working in the field of nonautonomous dynamical systems and their applications (population dynamics, oscillation theory, ecology, epidemiology, economics, biochemistry etc). The book should be accessible to graduate and PhD students who took courses in real analysis (including the elements of functional analysis, general topology) and with general background in dynamical systems and qualitative theory of differential/difference equations.
Nonautonomous Dynamics
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Author : David N. Cheban
language : en
Publisher: Springer Nature
Release Date : 2020-01-22
Nonautonomous Dynamics written by David N. Cheban and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-22 with Mathematics categories.
This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations. The content is developed over six chapters, providing a thorough introduction to the techniques used in the Chapters III-VI described by Chapter I-II. The author gives a systematic treatment of the basic mathematical theory and constructive methods for Nonautonomous Dynamics. They show how these diverse topics are connected to other important parts of mathematics, including Topology, Functional Analysis and Qualitative Theory of Differential/Difference Equations. Throughout the book a nice balance is maintained between rigorous mathematics and applications (ordinary differential/difference equations, functional differential equations and partial difference equations). The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).
Global Attractors Of Nonautonomous Dissipative Dynamical Systems
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Author : David N Cheban
language : en
Publisher: World Scientific
Release Date : 2004-11-29
Global Attractors Of Nonautonomous Dissipative Dynamical Systems written by David N Cheban and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-29 with Mathematics categories.
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.
Global Attractors Of Non Autonomous Dissipative Dynamical Systems
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Author : David N. Cheban
language : en
Publisher: World Scientific
Release Date : 2004
Global Attractors Of Non Autonomous Dissipative Dynamical Systems written by David N. Cheban and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Global Attractors Of Non Autonomous Dynamical And Control Systems 2nd Edition
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Author : David N Cheban
language : en
Publisher: World Scientific
Release Date : 2014-12-15
Global Attractors Of Non Autonomous Dynamical And Control Systems 2nd Edition written by David N Cheban and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Mathematics categories.
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.
Analysis Applications And Computations
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Author : Uwe Kähler
language : en
Publisher: Springer Nature
Release Date : 2023-10-30
Analysis Applications And Computations written by Uwe Kähler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-30 with Mathematics categories.
This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.
Dynamical Systems In Population Biology
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Author : Xiao-Qiang Zhao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-05
Dynamical Systems In Population Biology written by Xiao-Qiang Zhao 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 2013-06-05 with Mathematics categories.
Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.
Attractors For Infinite Dimensional Non Autonomous Dynamical Systems
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Author : Alexandre Carvalho
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-26
Attractors For Infinite Dimensional Non Autonomous Dynamical Systems written by Alexandre Carvalho 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 2012-09-26 with Mathematics categories.
The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.
Stability And Bifurcation Theory For Non Autonomous Differential Equations
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Author : Anna Capietto
language : en
Publisher: Springer
Release Date : 2012-12-14
Stability And Bifurcation Theory For Non Autonomous Differential Equations written by Anna Capietto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.
Differential And Difference Equations With Applications
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Author : Sandra Pinelas
language : en
Publisher: Springer
Release Date : 2018-05-08
Differential And Difference Equations With Applications written by Sandra Pinelas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-08 with Mathematics categories.
This book gathers papers from the International Conference on Differential & Difference Equations and Applications 2017 (ICDDEA 2017), held in Lisbon, Portugal on June 5-9, 2017. The editors have compiled the strongest research presented at the conference, providing readers with valuable insights into new trends in the field, as well as applications and high-level survey results. The goal of the ICDDEA was to promote fruitful collaborations between researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with a special emphasis on applications.