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Dynamical Systems in Population Biology
by Xiao-Qiang ZhaoPopulation dynamics is an important subject in mathematical biology. A cen#65533; 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.
Dynamical Systems in Theoretical Perspective: Poland December 11 -14 2017 (Springer Proceedings in Mathematics & Statistics #248)
by Jan AwrejcewiczThis book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life sciences. The book consists of contributed research chapters addressing a diverse range of problems. The issues discussed include (among others): numerical-analytical algorithms for nonlinear optimal control problems on a large time interval; gravity waves in a reservoir with an uneven bottom; value distribution and growth of solutions for certain Painlevé equations; optimal control of hybrid systems with sliding modes; a mathematical model of the two types of atrioventricular nodal reentrant tachycardia; non-conservative instability of cantilevered nanotubes using the Cell Discretization Method; dynamic analysis of a compliant tensegrity structure for use in a gripper application; and Jeffcott rotor bifurcation behavior using various models of hydrodynamic bearings.
Dynamical Systems on 2- and 3-Manifolds
by Viacheslav Z. Grines Timur V. Medvedev Olga V. PochinkaThis book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds. The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.
Dynamical Systems on Networks
by Mason A. Porter James P. GleesonThis volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on "simple" situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics, and co-Director of MACSI, at the University of Limerick, Ireland.
Dynamical Systems with Applications using Python
by Stephen LynchThis textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams.After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential.
Dynamical Systems: Theories and Applications
by Zeraoulia ElhadjChaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.
Dynamical Tunneling: Theory and Experiment
by Srihari Keshavamurthy Peter SchlagheckA prominent aspect of quantum theory, tunneling arises in a variety of contexts across several fields of study, including nuclear, atomic, molecular, and optical physics and has led to technologically relevant applications in mesoscopic science. Exploring mechanisms and consequences, Dynamical Tunneling: Theory and Experiment presents the work of i
Dynamically Structured Flow in Pulsed Fluidised Beds (Springer Theses)
by Kaiqiao WuThis book analyses the use of a pulsed gas flow to structure bubbling gas-solid fluidised beds and to induce a special fluidisation state, called "dynamically structured flow", as a promising approach to process intensification. It explores the properties of bubbles rising in staggered periodic arrays without direct interaction, assessing their size, separation, and velocity, and explains how a highly uniform, scalable flow offers tight control over the system hydrodynamics. These features are desirable, as they not only bypass engineering challenges occurring in traditional operations, such as maldistribution and non-uniform contact, but also allow to decouple conflicting design objectives, such as mixing and gas-solid contact. The thesis also presents computational simulations which reveal the periodic transitions of the particulate phase between fluid-like and solid-like behaviour. This book will be of interest to researchers, engineers, and graduate students alike, particularly those working in industrial drying, combustion, and chemical production.
Dynamics Near Quantum Criticality in Two Space Dimensions
by Snir GazitThis work addresses dynamical aspects of quantum criticality in two space dimensions. It probes two energy scales: the amplitude (Higgs) mode, which describes fluctuations of the order parameter amplitude in the broken symmetry phase and the dual vortex superfluid stiffness. The results demonstrate that the amplitude mode can be probed arbitrarily close to criticality in the universal line shape of the scalar susceptibility and the optical conductivity. The hallmark of quantum criticality is the emergence of softening energy scales near the phase transition. In addition, the author employs the charge-vortex duality to show that the capacitance of the Mott insulator near the superfluid to insulator phase transition serves as a probe for the dual vortex superfluid stiffness. The numerical methods employed are described in detail, in particular a worm algorithm for O(N) relativistic models and methods for numerical analytic continuation of quantum Monte Carlo data. The predictions obtained are particularly relevant to recent experiments in cold atomic systems and disordered superconductors.
Dynamics Of Quantised Vortices In Superfluids
by Edouard B. SoninA comprehensive overview of the basic principles of vortex dynamics in superfluids, this book addresses the problems of vortex dynamics in all three superfluids available in laboratories (4He, 3He, and BEC of cold atoms) alongside discussions of the elasticity of vortices, forces on vortices, and vortex mass. Beginning with a summary of classical hydrodynamics, the book guides the reader through examinations of vortex dynamics from large scales to the microscopic scale. Topics such as vortex arrays in rotating superfluids, bound states in vortex cores and interaction of vortices with quasiparticles are discussed. The final chapter of the book considers implications of vortex dynamics to superfluid turbulence using simple scaling and symmetry arguments. Written from a unified point of view that avoids complicated mathematical approaches, this text is ideal for students and researchers working with vortex dynamics in superfluids, superconductors, magnetically ordered materials, neutron stars and cosmological models.
Dynamics On and Of Complex Networks
by Animesh Mukherjee Andreas Deutsch Niloy GangulyThis self-contained book systematically explores the statistical dynamics on and of complex networks having relevance across a large number of scientific disciplines. The theories related to complex networks are increasingly being used by researchers for their usefulness in harnessing the most difficult problems of a particular discipline. The book is a collection of surveys and cutting-edge research contributions exploring the interdisciplinary relationship of dynamics on and of complex networks. Topics covered include complex networks found in nature--genetic pathways, ecological networks, linguistic systems, and social systems--as well as man-made systems such as the World Wide Web and peer-to-peer networks. The contributed chapters in this volume are intended to promote cross-fertilization in several research areas, and will be valuable to newcomers in the field, experienced researchers, practitioners, and graduate students interested in systems exhibiting an underlying complex network structure in disciplines such as computer science, biology, statistical physics, nonlinear dynamics, linguistics, and the social sciences.
Dynamics On and Of Complex Networks III: Machine Learning and Statistical Physics Approaches (Springer Proceedings in Complexity)
by Bivas Mitra Fakhteh Ghanbarnejad Rishiraj Saha Roy Fariba Karimi Jean-Charles DelvenneThis book bridges the gap between advances in the communities of computer science and physics--namely machine learning and statistical physics. It contains diverse but relevant topics in statistical physics, complex systems, network theory, and machine learning. Examples of such topics are: predicting missing links, higher-order generative modeling of networks, inferring network structure by tracking the evolution and dynamics of digital traces, recommender systems, and diffusion processes.The book contains extended versions of high-quality submissions received at the workshop, Dynamics On and Of Complex Networks (doocn.org), together with new invited contributions. The chapters will benefit a diverse community of researchers. The book is suitable for graduate students, postdoctoral researchers and professors of various disciplines including sociology, physics, mathematics, and computer science.
Dynamics On and Of Complex Networks, Volume 2: Applications to Time-Varying Dynamical Systems
by Animesh Mukherjee Niloy Ganguly Bivas Mitra Fernando Peruani Monojit ChoudhuryThis self-contained book systematically explores the statistical dynamics on and of complex networks with a special focus on time-varying networks. In the constantly changing modern world, there is an urgent need to understand problems related to systems that dynamically evolve in either structure or function, or both. This work is an attempt to address such problems in the framework of complex networks. Dynamics on and of Complex Networks, Volume 2: Applications to Time-Varying Dynamical Systems is a collection of surveys and cutting-edge research contributions exploring key issues, challenges, and characteristics of dynamical networks that emerge in various complex systems. Toward this goal, the work is thematically organized into three main sections with the primary thrust on time-varying networks: Part I studies social dynamics; Part II focuses on community identification; and Part III illustrates diffusion processes. The contributed chapters in this volume are intended to promote cross-fertilization in several research areas and will be valuable to newcomers in the field, experienced researchers, practitioners, and graduate students interested in pursuing research in dynamical networks with applications to computer science, statistical physics, nonlinear dynamics, linguistics, and the social sciences. This volume follows Dynamics On and Of Complex Networks: Applications to Biology, Computer Science, and the Social Sciences (2009), ISBN 978-0-8176-4750-6.
Dynamics and Balancing of Multibody Systems: Application to Rural and Robotic Systems
by Subir Kumar Saha Vinay Gupta Himanshu ChaudharyThe book describes the methodologies for dynamics formulation, balancing, and optimizing dynamic quantities of multibody systems, such as mechanisms and robots. The writing equations of motion of multibody systems are simplified by using Decoupled Natural Orthogonal Complementary (DeNOC) matrices-based methodology originally proposed by the second author. Writing equations of motion using a DeNOC based approach enables the analytical expressions of even complicated systems which provide better physical insights of the system at-hand. The DeNOC based dynamics formulation of multibody systems is extended from system of continuum rigid-link to discrete equivalent system of point-masses coined as DeNOC-P. The dynamics formulation representing a link as point-masses is exploited to minimize the dynamic quantities shaking forces, shaking moments, or driving torques/forces by optimizing the mass redistribution of the link. Several numerical examples, such as carpet scraping machine, PUMA robot, Stewart platform, etc., are illustrated. The book also demonstrates a shape optimization methodology to realize the link with optimized mass redistribution. This textbook can be prescribed for teaching a course on dynamics and balancing of multibody systems at undergraduate and postgraduate level.
Dynamics and Bioavailability of Heavy Metals in the Rootzone
by H. Magdi SelimConcerns regarding heavy metal contamination in terrestrial ecosystems have prompted increasing efforts on limiting their bioavailability in the root zone. The complexity of the hydrologic system gives rise to the need for understanding the fate and transport of trace elements in the soil-water-plant environment. Dynamics and Bioavailability of Hea
Dynamics and Characterization of Composite Quantum Systems
by Manuel GessnerThis thesis sheds new light on the fascinating properties of composite quantum systems. Quantum systems of different sizes, ranging from small bipartite systems to large many-body ensembles, can be studied with the help of modern quantum optical experiments. These experiments make it possible to observe a broad variety of striking features, including nonclassical correlations, complex dynamics and quantum phase transitions. By adopting the complementary perspectives of quantum information theory, quantum chemistry and many-body theory, the thesis develops new methods for the efficient characterization and description of interacting, composite quantum systems.
Dynamics and Control of Advanced Structures and Machines
by Michael Krommer Hans Irschik Alexander BelyaevThe papers in this volume present and discuss the frontiers in the mechanics of controlled machines and structures. They are based on papers presented at the International Workshop on Advanced Dynamics and Model Based Control of Structures and Machines held in Vienna in September 2015. The workshop continues a series of international workshops held in Linz (2008) and St. Petersburg (2010).
Dynamics and Control of Advanced Structures and Machines: Contributions from the 3rd International Workshop, Perm, Russia (CISM International Centre for Mechanical Sciences #444)
by Alexander K. Belyaev Michael Krommer Hans Irschik Valerii P. MatveenkoThe volume includes 30 contributions from the 3rd International Workshop on Advanced Dynamics and Model Based Control of Structures and Machines representing the frontiers in the mechanics of controlled machines and structures. The Workshop, held in Perm, Russia in September 2017 continued a series of international workshops, starting in with the Japan - Austria Joint Workshop on Mechanics and Model Based Control of Smart Materials and Structures, the Russia - Austria Joint Workshop on Advanced Dynamics and Model Based Control of Structures and Machines and the first two editions of the International Workshop on Advanced Dynamics and Model Based Control of Structures and Machines. The previous workshops took place in Linz, Austria in September 2008 and April 2010, in St. Petersburg, Russia in July 2012 and in Vienna, Austria in September 2015. The up-to-date contributions are authored by internationally re-known leading experts in dynamics and control representing a broad spectrum of topics in the field of Advanced Structures and Machines; both, with respect to theoretical aspects as well as applications to contemporary engineering problems.
Dynamics and Control of Lorentz-Augmented Spacecraft Relative Motion
by Xu Huang Ye Yan Yueneng YangThis book develops a dynamical model of the orbital motion of Lorentz spacecraft in both unperturbed and J2-perturbed environments. It explicitly discusses three kinds of typical space missions involving relative orbital control: spacecraft hovering, rendezvous, and formation flying. Subsequently, it puts forward designs for both open-loop and closed-loop control schemes propelled or augmented by the geomagnetic Lorentz force. These control schemes are entirely novel and represent a significantly departure from previous approaches.
Dynamics and Control of Mechanical Systems in Offshore Engineering
by Shuzhi Sam Ge Wei He Bernard Voon Ee How Yoo Sang ChooDynamics and Control of Mechanical Systems in Offshore Engineering is a comprehensive treatment of marine mechanical systems (MMS) involved in processes of great importance such as oil drilling and mineral recovery. Ranging from nonlinear dynamic modeling and stability analysis of flexible riser systems, through advanced control design for an installation system with a single rigid payload attached by thrusters, to robust adaptive control for mooring systems, it is an authoritative reference on the dynamics and control of MMS. Readers will gain not only a complete picture of MMS at the system level, but also a better understanding of the technical considerations involved and solutions to problems that commonly arise from dealing with them. The text provides: · a complete framework of dynamical analysis and control design for marine mechanical systems; · new results on the dynamical analysis of riser, mooring and installation systems together with a general modeling method for a class of MMS; · a general method and strategy for realizing the control objectives of marine systems with guaranteed stability the effectiveness of which is illustrated by extensive numerical simulation; and · approximation-based control schemes using neural networks for installation of subsea structures with attached thrusters in the presence of time-varying environmental disturbances and parametric uncertainties. Most of the results presented are analytical with repeatable design algorithms with proven closed-loop stability and performance analysis of the proposed controllers is rigorous and detailed. Dynamics and Control of Mechanical Systems in Offshore Engineering is primarily intended for researchers and engineers in the system and control community, but graduate students studying control and marine engineering will also find it a useful resource as will practitioners working on the design, running or maintenance of offshore platforms.
Dynamics and Control of Trajectory Tubes
by Alexander B. Kurzhanski Pravin VaraiyaThis monograph presents theoretical methods involving the Hamilton-Jacobi-Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control. The emphasis is on issues of reachability, feedback control synthesis under complex state constraints, hard or double bounds on controls, and performance in finite time. Guaranteed state estimation, output feedback control, and hybrid dynamics are also discussed. Although the focus is on systems with linear structure, the authors indicate how to apply each approach to nonlinear and nonconvex systems. The main theoretical results lead to computational schemes based on extensions of ellipsoidal calculus that provide complete solutions to the problems. These computational schemes in turn yield software tools that can be applied effectively to high-dimensional systems. Ellipsoidal Techniques for Problems of Dynamics and Control: Theory and Computation will interest graduate and senior undergraduate students, as well as researchers and practitioners interested in control theory, its applications, and its computational realizations.
Dynamics and Defects in Liquid Crystals: A Festschrift in Honor of Alfred Saupe
by Patricia E. CladisDuring his distinguished scientific career, Alfred Saupe made important contributions to liquid crystal research, laying the groundwork on which much of the current knowledge and research in the physics of liquid crystals is based. This volume features papers presented by Prof. Saupe's colleagues, students and friends at a festschrift in honor of his 70th birthday. In addition, a selection of Prof. Saupe's articles are reprinted in the original German and in English translation, offering the reader a unique opportunity to see both the early work of this important scientist and widespread effect of that work on later discoveries in liquid crystal physics.
Dynamics and Design of Space Nets for Orbital Capture
by Leping Yang Qingbin Zhang Ming Zhen Haitao LiuThis book covers the topics of theoretical principles, dynamics model and algorithm, mission analysis, system design and experimental studies of space nets system, aiming to provide an initial framework in this field and serve as a ready reference for those interested. Space nets system represents a forefront field in future development of aerospace technologies. However, it involves new challenges and problems such as nonlinear and distorted nets structure, complex rigid flexible coupling dynamics, orbital transfer of space flexible composite and dynamics control. Currently, no comprehensive books on space nets dynamics and design are available, so potential readers can get to know the working mechanism, dynamics elements, and mission design of the space nets system from a Chinese perspective.
Dynamics and Fault Diagnosis of Nonlinear Rotors and Impellers (Nonlinear Systems and Complexity #34)
by Jiazhong ZhangThis contributed volume presents recent developments in nonlinear dynamics applied to engineering. Specifically, the authors address stability and bifurcation in large-scale, complex rotor dynamic systems; periodic motions and their bifurcations in nonlinear circuit systems, fault diagnosis of complex engineering systems with nonlinear approaches, singularities in fluid-machinery and bifurcation analysis, nonlinear behaviors in rotor dynamic system with multi-mistuned blades, mode localization induced by mistuning in impellers with periodical and cyclic symmetry, and nonlinear behaviors in fluid-structure interaction and their control. These new results will maximize reader understand on the recent progress in nonlinear dynamics applied to large-scale, engineering systems in general and nonlinear rotors and impellers in particular.
Dynamics and Kinetics in Structural Biology: Unravelling Function Through Time-Resolved Structural Analysis
by Eaton E. Lattman Keith MoffatDynamics and Kinetics in Structural Biology Understand the latest experimental tools in structural biology with this pioneering work Structural biology seeks to understand the chemical mechanisms and functions of biological molecules, such as proteins, based on their atomic structures. Until recently, these structures have been studied only statically, using procedures which deliberately freeze atomic motion. However, freezing eliminates the rapid structural motions so essential to biological activity and function; the molecules are inactive. But with the recent development of X-ray free electron laser (XFEL) sources, efforts to conduct dynamic experiments have expanded using the principles of dynamics and kinetics to capture active biological molecules as they function. Dynamics and Kinetics in Structural Biology promotes the development of these experiments and their successful application. It grounds readers in the foundational principles of dynamics and kinetics; proceeds through extended discussions of experimental procedures and data analysis techniques; and explores experimental frontiers in structural dynamics. The book will aid researchers to gather and interpret cutting-edge data on the dynamic structure of biological molecules, under conditions where they retain their biological functions. Dynamics and Kinetics in Structural Biology offers readers: Authorship by founding figures in the field In-depth presentation of time-resolved X-ray crystallography, solution scattering, and more A pioneering contribution to a rapidly developing field of study Dynamics and Kinetics in Structural Biology is essential reading for graduate students, scientists, researchers and industry professionals engaged in structural studies of biological systems. Industry professionals considering dynamic studies in the development of new product lines will also benefit.