Download or read book Stability and Complex Dynamics in a Discrete Tatonnement Model written by Jacob K. Goeree and published by . This book was released on 1995 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability of Dynamical Systems written by and published by Springer Science & Business Media. This book was released on 2008 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.

Download or read book Discrete Dynamical Systems written by Oded Galor and published by Springer Science & Business Media. This book was released on 2007-05-17 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.

Download or read book The Stability of Dynamical Systems written by J. P. LaSalle and published by SIAM. This book was released on 1976-01-01 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to aspects of the theory of dynamical systems based on extensions of Liapunov's direct method. The main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations.

Download or read book Discrete Chaos written by Saber N. Elaydi and published by CRC Press. This book was released on 2007-11-09 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determi

Download or read book Stability and Stable Oscillations in Discrete Time Systems written by Aristide Halanay and published by CRC Press. This book was released on 2000-10-31 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications in

Download or read book Stability of Dynamical Systems written by Xiaoxin Liao and published by Elsevier. This book was released on 2007-08-01 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers

Download or read book Hybrid Dynamical Systems written by Rafal Goebel and published by Princeton University Press. This book was released on 2012-03-18 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Download or read book Stability Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk and published by Birkhäuser. This book was released on 2016-09-22 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “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.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

Download or read book Stability of Dynamical Systems written by Anthony N Michel and published by Birkhäuser. This book was released on 2007-11-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling a gap in the literature, this volume offers the first comprehensive analysis of all the major types of system models. Throughout the text, there are many examples and applications to important classes of systems in areas such as power and energy, feedback control, artificial neural networks, digital signal processing and control, manufacturing, computer networks, and socio-economics. Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in a huge variety of fields.

Download or read book Journal of Economic Literature written by and published by . This book was released on 1998 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability and Control of Large Scale Dynamical Systems written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2011-11-14 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Download or read book Discrete Dynamical Modeling written by James T. Sandefur and published by Oxford University Press, USA. This book was released on 1993 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to a wide range of techniques and applications used in dynamical mathematical modelling. Emphasizing algebraic concepts, the text encourages students to develop a different manner of thinking about mathematics in order to apply mathematical concepts to other fields.

Download or read book Stability Elements of the Theory and Application with Examples written by Anatoliy A Martynyuk and published by Sciendo. This book was released on 2020-12-20 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to familiarize the readers with basic concepts, and classic results of stability theory stated in a way as required by the rigorous rules of contemporary mathematics and, simultaneously, to introduce the learners to broad elds of not only the stability theory but also applications involved. The emphasis is put on various dynamical systems which are defined by different branches of science and through diverse areas of human activity but always with care not to exceed the basic classical approach in the presentation. All in all, the authors plan to combine the textbook-like with encyclopaedia-like content. Another special goal of the authors is to attract the reader's attention to those aspects of theories whose incomplete understanding may lead to inaccuracies or errors. Sometimes, anyway just as designed, the offered information is limited to the pure statements of facts without any proofs. The reader should consult the references to find out missing pieces of information. This book also makes use of numerical (computer) computations. Most of the material contained in the book has already been published, a large part in various works of the authors. Fragments of several chapters come from published works of other authors - some excerpts, particularly relating to basic concepts, and some classic results are taken from outside sources. The book is offered as a textbook for the college-level students or as an aid to the PhD students interested in practical problems of the stability theory. The prerequisites are not demanding - the basic knowledge of calculus, complex functions, and linear algebra which are covered in the suitable, elementary courses is required. The first two chapters include what is typically covered in most introductory courses for students. The first chapter contains definitions of various types of stability; the second commences classic stability theorems regarding ordinary differential equations, but the most basic, applicable in technical sciences. The linear equations are treated more broadly, which creates a foundation for the linear approximation of differential equations in the stability research. Chapter three deals with integral inequalities and their application to the stability studies. Integral inequalities, both linear and nonlinear, are effectively applied in the development of the direct Lyapunov method when the boundedness and stability of motion of nonlinear weakly coupled systems are studied. Chapter four is predominantly dedicated to the Lyapunov direct method. Still, some attention is also paid to the method of limiting equations because it can be used to study motion stability even in hopeless cases when other methods fail. The issue of constructing of the Lyapunov function is a key element in applications of the direct method, and this chapter provides several methods of constructing the function. In the end, a string of examples illustrating the use of the Lyapunov direct method is posted. Chapter five contains a detailed presentation of the comparison method and its use in the stability research. This method, being is essential part of the qualitative theory of equations, is particularly central in studies of largescale systems. In the method, some differential inequalities and Lyapunov functions allow nonlinear transformations of the original system to an equation (a system or a matrix system) of a lower dimension. The idea of delimiting and estimating so-called stability domains is developed in chapter six, where also a qualitative comparison of different stability procedures is made. The evaluation of the efficiency of various methods is conducted by applying, in each case, the same vector norm as a measure of the distance between solutions - no surprise the Lyapunov direct method wins the competition. The contrast between various method results is shown using an example of a simple second-order differential equation. Moreover, for linear systems, the notion of the best Lyapunov function is made. Manifolds of non-holonomic equations of motion are in the focus of chapter seven. Application of topological manifolds and mapping techniques prove to be effective tools in the stability research that extends more and more to advanced fields of mathematics. The chapter reviews specific applications of the Lyapunov direct method to investigations of invariant manifolds and some practical results of the topological fixed point theory. Chapter eight deals with recurrence equations, difference equations, and difference inequalities that mainly are associated with discrete dynamic systems. These types of models are usually obtained by converting the time-continuous dynamics into discrete-time dynamics by employing the Poincare-type mappings. The main objective is the stability investigation of solutions and its estimates. Chapter nine is limited to a short overview of some stability issues for delay differential equations modelling some practical processes and systems with aftereffect phenomena - the main worry is about the compensation for the loss of stability due to delay in the system. Linear models are discussed, but the emphasis is put on Lyapunov functionals for nonlinear equations. Chapter ten on partial differential equations, not including the means of discretization to the stability analysis, uses an approach based on the utilization Lyapunov functionals. The Lyapunov theory is exercised here in relation to a particular class of continuous models - it is an outline of some techniques rather than the methodology. The presented here approach is anecdotal, and it is based on specific cases and examples. Chapter eleven presents some samples of the probabilistic approach to stability matters. This category of problems is necessary when in the modelling process, it turns out that the excitations are not clear, not defined, or not repeatable. In the present considerations, the stability study is reduced to examining the stability of the trivial solution, and the focus is on the almost-sure probability. The last chapter provides a brief introduction to themes of chaos, focusing on the dependence of chaos on the Lyapunov exponent. The irregular behaviour of solutions of motion which is identified with chaos is not due to stochastic forcing or sensitive dependence on initial conditions. The real reason for it is the exponential rate of the distance between the trajectories due to nonlinearities of the system - the Lyapunov exponent is a measure of it.

Download or read book Stability Theory of Dynamical Systems written by Jacques Leopold Willems and published by . This book was released on 1970 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discrete and Switching Dynamical Systems written by Albert C J Luo and published by L& H Scientific Publishing. This book was released on 2011-12-01 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete and Switching Dynamical Systems is a unique book about stability and its switching complexity in discrete dynamical systems, and provides a simple and concise view of the theory of stability and bifurcation in nonlinear discrete dynamical systems. Linear discrete systems with repeated eigenvalues are presented as an introduction. Higher-order singularity, stability and bifurcations in nonlinear discrete dynamical systems are presented. Several examples are presented to illustrate chaos fractality and complete dynamics of nonlinear discrete dynamical systems. Switching systems with transports are discussed comprehensively as a general fashion to present continuous and discrete mixed systems, and mapping dynamics, grazing phenomena and strange attractor fragmentation are also presented for a better understanding of regularity and complexity in discrete, switching and discontinuous dynamical systems. This book is written as a textbook or reference book for university students, professors and researchers in applied mathematics, physics, engineering, economics dynamics and finance. Albert C.J. Luo is an internationally recognized professor in nonlinear dynamics and mechanics. He worked at Southern Illinois University Edwardsville, USA. His principal research interests lie in the fields of Hamiltonian chaos, nonlinear mechanics, and discontinuous dynamical systems. A different view of stability and bifurcations in discrete dynamical systemsHigher order singularity, stability switching complexity and bifurcationsChaos fractality and complete dynamicsHow to construct mappings from physical systemsMapping dynamics, grazing invariance and strange attractor fragmentationUser friendly presentation and intuitive illustrationsWide audience due to instructive and comprehensive examples

Download or read book Analytical Dynamics of Discrete Systems written by R. Rosenberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is to serve as a text for engineering students at the senior or beginning graduate level in a second course in dynamics. It grew out of many years experience in teaching such a course to senior students in mechanical engineering at the University of California, Berkeley. While temperamentally disinclined to engage in textbook writing, I nevertheless wrote the present volume for the usual reason-I was unable to find a satisfactory English-language text with the content covered in my inter mediate course in dynamics. Originally, I had intended to fit this text very closely to the content of my dynamics course for seniors. However, it soon became apparent that that course reflects too many of my personal idiosyncracies, and perhaps it also covers too little material to form a suitable basis for a general text. Moreover, as the manuscript grew, so did my interest in certain phases of the subject. As a result, this book contains more material than can be studied in one semester or quarter. My own course covers Chapters 1 to 5 (Chapters 1,2, and 3 lightly) and Chapters 8 to 20 (Chapter 17 lightly).