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Author: Marat Akhmet
Publisher: Springer Science & Business Media
ISBN: 1441965815
Category : Mathematics
Languages : en
Pages : 185
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Book Description
Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems.
Author: Marat Akhmet
Publisher: Springer Science & Business Media
ISBN: 1441965815
Category : Mathematics
Languages : en
Pages : 185
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Book Description
Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems.
Author: Yury V. Orlov
Publisher: Springer Science & Business Media
ISBN: 1848009844
Category : Technology & Engineering
Languages : en
Pages : 333
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Book Description
Discontinuous Systems develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems, operating under uncertain conditions. While being primarily a research monograph devoted to the theory of discontinuous dynamic systems, no background in discontinuous systems is required; such systems are introduced in the book at the appropriate conceptual level. Being developed for discontinuous systems, the theory is successfully applied to their subclasses – variable-structure and impulsive systems – as well as to finite- and infinite-dimensional systems such as distributed-parameter and time-delay systems. The presentation concentrates on algorithms rather than on technical implementation although theoretical results are illustrated by electromechanical applications. These specific applications complete the book and, together with the introductory theoretical constituents bring some elements of the tutorial to the text.
Author:
Publisher: Springer Science & Business Media
ISBN: 0817644865
Category : Differentiable dynamical systems
Languages : en
Pages : 516
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Book Description
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.
Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 364222461X
Category : Science
Languages : en
Pages : 700
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Book Description
“Discontinuous Dynamical Systems” presents a theory of dynamics and flow switchability in discontinuous dynamical systems, which can be as the mathematical foundation for a new dynamics of dynamical system networks. The book includes a theory for flow barriers and passability to boundaries in discontinuous dynamical systems that will completely change traditional concepts and ideas in the field of dynamical systems. Edge dynamics and switching complexity of flows in discontinuous dynamical systems are explored in the book and provide the mathematical basis for developing the attractive network channels in dynamical systems. The theory of bouncing flows to boundaries, edges and vertexes in discontinuous dynamical systems with multi-valued vector fields is described in the book as a “billiard” theory of dynamical system networks. The theory of dynamical system interactions in discontinued dynamical systems can be used as a general principle in dynamical system networks, which is applied to dynamical system synchronization. The book represents a valuable reference work for university professors and researchers in applied mathematics, physics, mechanics, and control. Dr. Albert C.J. Luo is an internationally respected professor in nonlinear dynamics and mechanics, and he works at Southern Illinois University Edwardsville, USA.
Author: A.F. Filippov
Publisher: Springer Science & Business Media
ISBN: 9401577935
Category : Mathematics
Languages : en
Pages : 315
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Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 1461415233
Category : Mathematics
Languages : en
Pages : 500
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Book Description
Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
Author: Mario Bernardo
Publisher: Springer Science & Business Media
ISBN: 1846287081
Category : Mathematics
Languages : en
Pages : 497
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Book Description
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
Author: Vladimir Andreevich I?A?kubovich
Publisher: World Scientific
ISBN: 9812387196
Category : Mathematics
Languages : en
Pages : 351
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Book Description
This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman-Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines.
Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 1461415241
Category : Technology & Engineering
Languages : en
Pages : 503
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Book Description
Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
Author: Mike R. Jeffrey
Publisher: Springer
ISBN: 3030021076
Category : Mathematics
Languages : en
Pages : 531
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Book Description
The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to earthquakes. From individual decisions to economic crashes. Where discontinuities occur, determinacy is inevitably lost. Typically the physical laws of such change are poorly understood, and too ill-defined for standard mathematics. Discontinuities offer a way to make the bounds of scientific knowledge a part of the model, to analyse a system with detail and rigour, yet still leave room for uncertainty. This is done without recourse to stochastic modeling, instead retaining determinacy as far as possible, and focussing on the geometry of the many outcomes that become possible when it breaks down. In this book the foundations of `piecewise-smooth dynamics' theory are rejuvenated, given new life through the lens of modern nonlinear dynamics and asymptotics. Numerous examples and exercises lead the reader through from basic to advanced analytical methods, particularly new tools for studying stability and bifurcations. The book is aimed at scientists and engineers from any background with a basic grounding in calculus and linear algebra. It seeks to provide an invaluable resource for modeling discontinuous systems, but also to empower the reader to develop their own novel models and discover as yet unknown phenomena.
