- Table View
- List View
Dynamical Systems with Applications using MATLAB®
by Stephen LynchThis textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox® and the Symbolic Math toolbox®, including MuPAD. Features new to the second edition include · sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization; · chapters on image processing and binary oscillator computing; · hundreds of new illustrations, examples, and exercises with solutions; and · over eighty up-to-date MATLAB program files and Simulink model files available online. These files were voted MATLAB Central Pick of the Week in July 2013. The hands-on approach of Dynamical Systems with Applications using MATLAB, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equations. It will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and physics. Praise for the first edition Summing up, it can be said that this text allows the reader to have an easy and quick start to the huge field of dynamical systems theory. MATLAB/SIMULINK facilitate this approach under the aspect of learning by doing. --OR News/Operations Research Spectrum The MATLAB programs are kept as simple as possible and the author's experience has shown that this method of teaching using MATLAB works well with computer laboratory classes of small sizes. . . . I recommend 'Dynamical Systems with Applications using MATLAB' as a good handbook for a diverse readership: graduates and professionals in mathematics, physics, science and engineering. --Mathematica
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, Bifurcation Analysis and Applications: Penang, Malaysia, August 6–13, 2018 (Springer Proceedings in Mathematics & Statistics #295)
by Mohd Hafiz Mohd Norazrizal Aswad Abdul Rahman Nur Nadiah Abd Hamid Yazariah Mohd YatimThis book is the result of Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation studies in tracking both stable and unstable steady states and bifurcation points to gain better understanding of the dynamics of the systems. The SEAMS School 2018 on DySBA was held in Penang from 6th to 13th August at the School of Mathematical Sciences, Universiti Sains Malaysia.The SEAMS Schools are part of series of intensive study programs that aim to provide opportunities for an advanced learning experience in mathematics via planned lectures, contributed talks, and hands-on workshop.This book will appeal to those postgraduates, lecturers and researchers working in the field of dynamical systems and their applications. Senior undergraduates in Mathematics will also find it useful.
Dynamical Systems: Differential Equations, Maps, and Chaotic Behaviour (Chapman Hall/crc Mathematics Ser. #5)
by C.M. PlaceThis text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams) to develop the material, including a treatment of chaotic behavior.The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations.Applications in physics, engineering, and geology are considered and introductions to fractal imaging and cellular automata are given.
Dynamical Systems: Modelling
by Jan AwrejcewiczThe book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Å ódź, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.
Dynamical Systems: Stability, Symbolic Dynamics, and Chaos (Studies in Advanced Mathematics)
by Clark RobinsonSeveral distinctive aspects make Dynamical Systems unique, including:treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student
Dynamical Systems: Theoretical and Experimental Analysis
by Jan AwrejcewiczThe book is the second volume of a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Å ódź, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.
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 Zeta Functions and Dynamical Determinants for Hyperbolic Maps: A Functional Approach (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge / A Series Of Modern Surveys In Mathematics Ser. #68)
by Viviane BaladiThe spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations: VIASM 2016 (Lecture Notes in Mathematics #2183)
by Nam Q. Le Hiroyoshi Mitake Hung V. TranHiroyoshi Mitake Hung V. TranConsisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton–Jacobi equations.
Dynamically Coupled Rigid Body-Fluid Flow Systems
by Banavara N. ShashikanthThis book presents a unified study of dynamically coupled systems involving a rigid body and an ideal fluid flow from the perspective of Lagrangian and Hamiltonian mechanics. It compiles theoretical investigations on the topic of dynamically coupled systems using a framework grounded in Kirchhoff’s equations. The text achieves a balance between geometric mechanics, or the modern theories of reduction of Lagrangian and Hamiltonian systems, and classical fluid mechanics, with a special focus on the applications of these principles. Following an introduction to Kirchhoff’s equations of motion, the book discusses several extensions of Kirchhoff’s work, particularly related to vortices. It addresses the equations of motions of these systems and their Lagrangian and Hamiltonian formulations. The book is suitable to mathematicians, physicists and engineers with a background in Lagrangian and Hamiltonian mechanics and theoretical fluid mechanics. It includes a brief introductory overview of geometric mechanics in the appendix.
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 Analysis of Alignment Models of Collective Behavior (Nečas Center Series)
by Roman ShvydkoyThis book introduces a class of alignment models based on the so-called Cucker-Smale system as well as its kinetic and hydrodynamic counterparts. Cutting edge research in the area of collective behavior is presented, including emerging techniques from fluid mechanics, fractional analysis, and kinetic theory. Analytical aspects are highlighted throughout, such as regularity theory and long time behavior of solutions. Featuring open problems, readers will be motivated to apply these breakthrough methods to future research. The chapters offer an overview of state of the art research with introductions to core concepts. Chapter One introduces the central focus of the book: The agent-based Cucker-Smale system. Further agent-based systems and alignment systems are covered in chapters Two and Three. Following this are chapters covering the kinetic and hydrodynamic variants of the Cucker-Smale system. The core well-posedness theory of both smooth and singular models is then presented. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems. Dynamics and Analysis of Alignment Models of Collective Behavior is ideal for graduate students and researchers studying PDEs, especially those interested in the active areas of collective behavior and alignment models.
Dynamics and Analytic Number Theory
by Dzmitry Badziahin Alexander Gorodnik Norbert PeyerimhoffWritten by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.
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 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 Mechanisms Design for Technology Students: A Project-Based Approach (Synthesis Lectures on Mechanical Engineering)
by Anthony D´Angelo Jr.The book reviews the algebra, trigonometry, and basic calculus students need to be successful in solving problems. Next, a review of kinematics and Newton’s laws are discussed, and numerous examples are solved. Mechanisms include the slider crank, offset slider crank, gears and gear trains, belts and chains, and cams. A graphical and analytical approach is taken when covering slider crank mechanisms. The book uses vectors and Kennedy's theorem to solve a variety of included examples. Gears and gear trains as well as belts and chains are discussed. Finally, cams using graphical and analytical techniques are introduced. The concluding chapter gives multiple projects used in the class to capture the lectures and computer modeling using Excel and MATLAB.
Dynamics and Relativity
by Jeffrey Forshaw Gavin SmithA new title in the Manchester Physics Series, this introductory text emphasises physical principles behind classical mechanics and relativity. It assumes little in the way of prior knowledge, introducing relevant mathematics and carefully developing it within a physics context. Designed to provide a logical development of the subject, the book is divided into four sections, introductory material on dynamics, and special relativity, which is then followed by more advanced coverage of dynamics and special relativity. Each chapter includes problems ranging in difficulty from simple to challenging with?solutions for solving problems. Includes?solutions for solving problemsNumerous worked examples included throughout the bookMathematics is carefully explained and developed within a physics environmentSensitive to topics that can appear daunting or confusing
Dynamics and Stability of Continuous-Time Switched Linear Systems (Progress in Nonlinear Differential Equations and Their Applications #105)
by Mario Sigalotti Yacine Chitour Paolo MasonLinear switched systems are a fascinating field of research, with many theoretical questions arising from applications which require sophisticated mathematical tools for their resolution. This monograph presents a unified theoretical approach for the analysis of stability of continuous-time linear switched systems, organizing and optimizing results scattered throughout literature. Emphasis is placed on the development of a rigorous and complete mathematical theory. In addition to fundamental tools such as common Lyapunov functions, converse Lyapunov theorems, and maximal Lyapunov exponents, the concept of Barabanov norm is also discussed. While this is now well understood from a theoretical point of view, it has not received much attention in more application-focused settings, likely because this fundamental object was developed in the context of arbitrary switches but has no immediate equivalent for classes of switching signals subject to various constraints (dwell time, persistent excitation, etc.). One of the aims of this text is to bridge this gap as far as possible by explaining how the main features of Barabanov norms can be generalized for classes of constrained switchings. Throughout the text, the authors maintain a general point of view, rather than treating classes of switching signals separately, by developing an axiomatic approach and identifying structural properties of these classes that allow crucial aspects of the Barabanov norm to be extended. This monograph will be a valuable resource for mathematicians and control engineers interested in continuous-time switched linear systems, as well as a definitive reference for more experienced researchers.
Dynamics in Logic and Language: Third Tsinghua Interdisciplinary Workshop on Logic, Language, and Meaning, TLLM 2022, Virtual Event, April 1–4, 2022, Revised Selected Papers (Lecture Notes in Computer Science #13524)
by Mingming Liu Dun Deng Dag Westerståhl Kaibo XieEdited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the Third Tsinghua Interdisciplinary Workshop on Logic, Language, and Meaning, TLLM 2022, which was held virtually in April 2022.The 9 full papers presented in this volume were carefully reviewed and selected from 13 submissions. The workshop covers a wide range of topics such as dynamic semantics, logical dynamics, Dynamic Epistemic Logic, Discourse Representation Theory, formal semantics, free choice inference, update semantics, and donkey sentences.
Dynamics in Logistics
by Bernd Scholz-Reiter Hans-Jörg Kreowski Klaus-Dieter ThobenThe volume comprises the proceedings of the third International Conference on Dynamics in Logistics LDIC 2012. The scope of the conference targeted the identification, analysis, and description of the dynamics of logistic processes and networks. The spectrum ranged from the modeling and planning of processes and innovative methods like autonomous control and knowledge management to the new technologies provided by radio frequency identification, mobile communication, and networking. The growing dynamics in the area of logistics poses completely new challenges: Logistic processes and networks must rapidly and flexibly adapt to continuously changing conditions. LDIC 2012 provided a venue for researchers from academia and industry interested in the technical advances in dynamics in logistics. The conference addressed research in logistics from a wide range of fields, e.g. engineering, computer science and operations research. The volume consists of two invited papers and of 49 contributed papers divided into various subjects including transport logistics, routing in dynamic logistic networks, modeling, simulation, optimization and collaboration in logistics, identification technologies, mathematical modeling in transport and production logistics, information, communication, risk and failure in logistic systems, autonomous control in logistic processes, global supply chains and industrial applications, and the Internet of Things in the context of logistics.
Dynamics in Logistics: Twenty-Five Years of Interdisciplinary Logistics Research in Bremen, Germany
by Herbert Kotzab Michael Freitag Nicole MegowThis open access book highlights the interdisciplinary aspects of logistics research. Featuring empirical, methodological, and practice-oriented articles, it addresses the modelling, planning, optimization and control of processes. Chiefly focusing on supply chains, logistics networks, production systems, and systems and facilities for material flows, the respective contributions combine research on classical supply chain management, digitalized business processes, production engineering, electrical engineering, computer science and mathematical optimization. To celebrate 25 years of interdisciplinary and collaborative research conducted at the Bremen Research Cluster for Dynamics in Logistics (LogDynamics), in this book hand-picked experts currently or formerly affiliated with the Cluster provide retrospectives, present cutting-edge research, and outline future research directions.
Dynamics in One Complex Variable
by John MilnorThis volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Latt#xC3;#xA9;s map has been made more inclusive, and the #xC3;0calle-Voronin theory of parabolic points is described. The r#xC3;#xA9;sidu it#xC3;#xA9;ratif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.