Nonautonomous Dynamical Systems In The Life Sciences

Author : Peter E. Kloeden,Christian Pötzsche
Publisher : Springer
Page : 314 pages
File Size : 55,5 Mb
Release : 2014-01-22
Category : Mathematics
ISBN : 9783319030807

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Nonautonomous Dynamical Systems in the Life Sciences by Peter E. Kloeden,Christian Pötzsche Pdf

Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.

Author : Peter E. Kloeden,Martin Rasmussen
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 45,5 Mb
Release : 2011-08-17
Category : Mathematics
ISBN : 9780821868713

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Nonautonomous Dynamical Systems by Peter E. Kloeden,Martin Rasmussen Pdf

The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.

Author : Peter Kloeden,Meihua Yang
Publisher : World Scientific
Page : 157 pages
File Size : 47,5 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9789811228674

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An Introduction To Nonautonomous Dynamical Systems And Their Attractors by Peter Kloeden,Meihua Yang Pdf

The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required.In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other.The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant.Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a 'Thousand Expert' Professorship at the Huazhong University of Science and Technology in Wuhan.

Author : Aneta Stefanovska,Peter V. E. McClintock
Publisher : Springer Nature
Page : 431 pages
File Size : 45,8 Mb
Release : 2021-05-05
Category : Science
ISBN : 9783030598051

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Physics of Biological Oscillators by Aneta Stefanovska,Peter V. E. McClintock Pdf

This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described. Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas.

Author : Tomislav Stankovski
Publisher : Springer Science & Business Media
Page : 145 pages
File Size : 43,5 Mb
Release : 2013-08-27
Category : Science
ISBN : 9783319007533

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Tackling the Inverse Problem for Non-Autonomous Systems by Tomislav Stankovski Pdf

This thesis presents a new method for following evolving interactions between coupled oscillatory systems of the kind that abound in nature. Examples range from the subcellular level, to ecosystems, through climate dynamics, to the movements of planets and stars. Such systems mutually interact, adjusting their internal clocks, and may correspondingly move between synchronized and non-synchronized states. The thesis describes a way of using Bayesian inference to exploit the presence of random fluctuations, thus analyzing these processes in unprecedented detail. It first develops the basic theory of interacting oscillators whose frequencies are non-constant, and then applies it to the human heart and lungs as an example. Their coupling function can be used to follow with great precision the transitions into and out of synchronization. The method described has the potential to illuminate the ageing process as well as to improve diagnostics in cardiology, anesthesiology and neuroscience, and yields insights into a wide diversity of natural processes.

Author : Meihua Yang (Professor of Mathematics),Peter E. Kloeden
Publisher : Unknown
Page : 144 pages
File Size : 40,5 Mb
Release : 2020
Category : Attractors (Mathematics)
ISBN : 9811228663

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An Introduction to Nonautonomous Dynamical Systems and Their Attractors by Meihua Yang (Professor of Mathematics),Peter E. Kloeden Pdf

Dynamical systems. Autonomous dynamical systems. Nonautonomous dynamical systems : processes. Skew product flows. Entire solutions and invariant sets -- Pullback attractors. Attractors. Nonautonomous equilibrium solutions. Attractors for processes. Examples of pullback attractors for processes. Attractors of skew product flows -- Forward attractors and attracting sets. Limitations of pullback attractors of processes. Forward attractors. Omega-limit sets and forward attracting sets -- Random aattractors. Random dynamical systems. Mean-square random dynamical systems.

Author : Xiao-Qiang Zhao
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 47,6 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780387217611

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Dynamical Systems in Population Biology by Xiao-Qiang Zhao Pdf

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.

Author : Yemon Choi,Matthew Daws,Gordon Blower
Publisher : Springer Nature
Page : 262 pages
File Size : 54,8 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 9783031380204

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Operators, Semigroups, Algebras and Function Theory by Yemon Choi,Matthew Daws,Gordon Blower Pdf

This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.

Author : Ezio Bartocci,Pietro Lio,Nicola Paoletti
Publisher : Springer
Page : 356 pages
File Size : 47,9 Mb
Release : 2016-09-03
Category : Computers
ISBN : 9783319451770

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Computational Methods in Systems Biology by Ezio Bartocci,Pietro Lio,Nicola Paoletti Pdf

This book constitutes the refereed proceedings of the 14th International Conference on Computational Methods in Systems Biology, CMSB 2016, held in Cambridge, UK, in September 2016. The 20 full papers, 3 tool papers and 9 posters presented were carefully reviewed and selected from 37 regular paper submissions. The topics include formalisms for modeling biological processes; models and their biological applications; frameworks for model verification, validation, analysis, and simulation of biological systems; high-performance computational systems biology and parallel implementations; model inference from experimental data; model integration from biological databases; multi-scale modeling and analysis methods; and computational approaches for synthetic biology.

Author : Dragutin T Mihailovic,Igor Balaž,Darko Kapor
Publisher : Elsevier
Page : 412 pages
File Size : 48,5 Mb
Release : 2016-10-31
Category : Science
ISBN : 9780444639233

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Time and Methods in Environmental Interfaces Modelling by Dragutin T Mihailovic,Igor Balaž,Darko Kapor Pdf

Time and Methods in Environmental Interfaces Modelling: Personal Insights considers the use of time in environmental interfaces modeling and introduce new methods, from the global scale (e.g. climate modeling) to the micro scale (e.g. cell and nanotubes modeling), which primarily arise from the personal research insights of the authors. As the field of environmental science requires the application of new fundamental approaches that can lead to a better understanding of environmental phenomena, this book helps necessitate new approaches in modeling, including category theory, that follow new achievements in physics, mathematics, biology, and chemistry. Includes the use of new mathematical tools, such as category theory, mathematical theory of general systems and formal concept analysis, matrix theory tools, stability analysis, and pseudospectra Presents new content related to time in relation to physics and biology Combines the word of an experienced author team with over 35 papers of collective experience

Author : Jeffrey Scott Barrett,Catherine M. T. Sherwin
Publisher : Frontiers Media SA
Page : 179 pages
File Size : 49,7 Mb
Release : 2022-10-21
Category : Science
ISBN : 9782832503119

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Insights in Obstetric and Pediatric Pharmacology: 2021 by Jeffrey Scott Barrett,Catherine M. T. Sherwin Pdf

Author : John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 46,6 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9781461445227

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Infinite Dimensional Dynamical Systems by John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi Pdf

​This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.​

Author : Tijana Bojić,Maurizio Acampa,Andreas Voss
Publisher : Frontiers Media SA
Page : 162 pages
File Size : 45,7 Mb
Release : 2021-06-01
Category : Science
ISBN : 9782889667932

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Cardiorespiratory Coupling - Novel Insights for Integrative Biomedicine by Tijana Bojić,Maurizio Acampa,Andreas Voss Pdf

Author : Anna Capietto,Peter Kloeden,Jean Mawhin,Sylvia Novo,Miguel Ortega
Publisher : Springer
Page : 314 pages
File Size : 44,6 Mb
Release : 2012-12-14
Category : Mathematics
ISBN : 9783642329067

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Stability and Bifurcation Theory for Non-Autonomous Differential Equations by Anna Capietto,Peter Kloeden,Jean Mawhin,Sylvia Novo,Miguel Ortega Pdf

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.

Author : Martin Wechselberger
Publisher : Springer Nature
Page : 143 pages
File Size : 53,7 Mb
Release : 2020-02-21
Category : Mathematics
ISBN : 9783030363994

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Geometric Singular Perturbation Theory Beyond the Standard Form by Martin Wechselberger Pdf

This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.