Discontinuous Systems

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Discontinuous Systems

Author : Yury V. Orlov
Publisher : Springer Science & Business Media
ISBN 13 : 1848009844
Total Pages : 333 pages
Book Rating : 4.8/5 (48 download)

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Book Synopsis Discontinuous Systems by : Yury V. Orlov

Download or read book Discontinuous Systems written by Yury V. Orlov and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Principles of Discontinuous Dynamical Systems

Author : Marat Akhmet
Publisher : Springer Science & Business Media
ISBN 13 : 1441965815
Total Pages : 176 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Principles of Discontinuous Dynamical Systems by : Marat Akhmet

Download or read book Principles of Discontinuous Dynamical Systems written by Marat Akhmet and published by Springer Science & Business Media. This book was released on 2010-08-26 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bifurcation and Chaos in Discontinuous and Continuous Systems

Author : Michal Fečkan
Publisher : Springer Science & Business Media
ISBN 13 : 3642182690
Total Pages : 378 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Bifurcation and Chaos in Discontinuous and Continuous Systems by : Michal Fečkan

Download or read book Bifurcation and Chaos in Discontinuous and Continuous Systems written by Michal Fečkan and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well. This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate students either studying oscillations of nonlinear mechanical systems or investigating vibrations of strings and beams, and electrical circuits by applying the modern theory of bifurcation methods in dynamical systems. Dr. Michal Fečkan is a Professor at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovakia. He is working on nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.

Vibration of Strongly Nonlinear Discontinuous Systems

Author : V.I. Babitsky
Publisher : Springer Science & Business Media
ISBN 13 : 3540444882
Total Pages : 415 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Vibration of Strongly Nonlinear Discontinuous Systems by : V.I. Babitsky

Download or read book Vibration of Strongly Nonlinear Discontinuous Systems written by V.I. Babitsky and published by Springer Science & Business Media. This book was released on 2012-11-02 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the systematic representation of the methods of analysis developed by the authors as applied to such systems. Particular features of dynamic processes in such systems are studied. Special attention is given to an analysis of different resonant phenomena taking unusual and diverse forms.

Discontinuous Dynamical Systems

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 364222461X
Total Pages : 692 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Discontinuous Dynamical Systems by : Albert C. J. Luo

Download or read book Discontinuous Dynamical Systems written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2012-04-07 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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.

Differential Equations with Discontinuous Righthand Sides

Author : A.F. Filippov
Publisher : Springer Science & Business Media
ISBN 13 : 9401577935
Total Pages : 315 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Differential Equations with Discontinuous Righthand Sides by : A.F. Filippov

Download or read book Differential Equations with Discontinuous Righthand Sides written by A.F. Filippov and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discontinuous Dynamical Systems on Time-varying Domains

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 3642002536
Total Pages : 228 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Discontinuous Dynamical Systems on Time-varying Domains by : Albert C. J. Luo

Download or read book Discontinuous Dynamical Systems on Time-varying Domains written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2009-11-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Discontinuous Dynamical Systems on Time-varying Domains" is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains, this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory, principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers, advanced undergraduate and graduate students in mathematics, physics and mechanics. Dr. Albert C. J. Luo is a professor at Southern Illinois University Edwardsville, USA. His research is involved in the nonlinear theory of dynamical systems. His main contributions are in the following aspects: a stochastic and resonant layer theory in nonlinear Hamiltonian systems, singularity on discontinuous dynamical systems, and approximate nonlinear theories for a deformable-body.

Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities

Author : Vladimir Andreevich I?A?kubovich
Publisher : World Scientific
ISBN 13 : 9812794239
Total Pages : 351 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities by : Vladimir Andreevich I?A?kubovich

Download or read book Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities written by Vladimir Andreevich I?A?kubovich and published by World Scientific. This book was released on 2004 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 KalmanOCoYakubovich 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. Sample Chapter(s). Chapter 1: Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides (455 KB). Contents: Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides; Auxiliary Algebraic Statements on Solutions of Matrix Inequalities of a Special Type; Dichotomy and Stability of Nonlinear Systems with Multiple Equilibria; Stability of Equilibria Sets of Pendulum-Like Systems. Readership: Upper level undergraduates, graduate students, academics, researchers and engineers involved with mechanics, electrical science and power systems."

Stability of Dynamical Systems

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0817644865
Total Pages : 516 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Stability of Dynamical Systems by :

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.

Discontinuous Control Systems

Author : Igor Boiko
Publisher : Springer Science & Business Media
ISBN 13 : 0817647538
Total Pages : 212 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Discontinuous Control Systems by : Igor Boiko

Download or read book Discontinuous Control Systems written by Igor Boiko and published by Springer Science & Business Media. This book was released on 2008-11-18 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides new insight on the problem of closed-loop performance and oscillations in discontinuous control systems, covering the class of systems that do not necessarily have low-pass filtering properties. The author provides a practical, yet rigorous and exact approach to analysis and design of discontinuous control systems via application of a novel frequency-domain tool: the locus of a perturbed relay system. Presented are a number of practical examples applying the theory to analysis and design of discontinuous control systems from various branches of engineering, including electro-mechanical systems, process control, and electronics. Discontinuous Control Systems is intended for readers who have knowledge of linear control theory and will be of interest to graduate students, researchers, and practicing engineers involved in systems analysis and design.

Investigation of Nonlinear Control Systems: Discontinuous control systems

Author : Nicolai Minorsky
Publisher :
ISBN 13 :
Total Pages : 688 pages
Book Rating : 4.X/5 (4 download)

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Book Synopsis Investigation of Nonlinear Control Systems: Discontinuous control systems by : Nicolai Minorsky

Download or read book Investigation of Nonlinear Control Systems: Discontinuous control systems written by Nicolai Minorsky and published by . This book was released on 1960 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Singularity and Dynamics on Discontinuous Vector Fields

Author : Albert C.J. Luo
Publisher : Elsevier
ISBN 13 : 9780080480930
Total Pages : 310 pages
Book Rating : 4.4/5 (89 download)

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Book Synopsis Singularity and Dynamics on Discontinuous Vector Fields by : Albert C.J. Luo

Download or read book Singularity and Dynamics on Discontinuous Vector Fields written by Albert C.J. Luo and published by Elsevier. This book was released on 2006-07-07 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones’ thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics. Challenging continuous Newton's dynamics Original theory and seeds of new researches in the field Wide spectrum of applications in science and engineering Systematic presentation and clear illustrations

Discontinuities in Ecosystems and Other Complex Systems

Author : Craig R. Allen
Publisher : Columbia University Press
ISBN 13 : 0231516827
Total Pages : 287 pages
Book Rating : 4.2/5 (315 download)

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Book Synopsis Discontinuities in Ecosystems and Other Complex Systems by : Craig R. Allen

Download or read book Discontinuities in Ecosystems and Other Complex Systems written by Craig R. Allen and published by Columbia University Press. This book was released on 2008-07-01 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the publication of C. S. Holling's seminal work on the relationship between animal body mass patterns and scale-specific landscape structure, ecologists began to explore the theoretical and applied consequences of discontinuities in ecosystems and other complex systems. Are ecosystems and their components continuously distributed and do they adhere to scaling laws, or are they discontinuous and more complex than early models would have us believe? The resulting propositions over the structure of complex systems sparked an ongoing debate regarding the mechanisms generating discontinuities and the statistical methods used for their detection. This volume takes the view that ecosystems and other complex systems are inherently discontinuous and that such fields as ecology, economics, and urban studies greatly benefit from this paradigm shift. Contributors present evidence of the ubiquity of discontinuous distributions in ecological and social systems and how their analysis provides insight into complex phenomena. The book is divided into three sections. The first focuses on background material and contrasting views concerning the discontinuous organization of complex systems. The second discusses discontinuous patterns detected in a number of different systems and methods for detecting them, and the third touches on the potential significance of discontinuities in complex systems. Science is still dominated by a focus on power laws, but the contributors to this volume are convinced power laws often mask the interesting dynamics of systems and that those dynamics are best revealed by investigating deviations from assumed power law distributions. In 2008, a grand conference on resilience was held in Stockholm, hosting 600 participants from around the world. There are now three big centers established with resilience, the most recent one being the Stockholm Resilience Center, with others in Australia (an international coral reef center), Arizona State University's new sustainability center focusing on anthropology, and Canada's emerging social sciences and resilience center. Activity continues to flourish in Alaska, South Africa, and the Untied Kingdom, and a new center is forming in Uruguay.

On Oscillations of Nonlinear Discontinuous Systems

Author : Chii-Yuh Chern
Publisher :
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.:/5 (29 download)

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Book Synopsis On Oscillations of Nonlinear Discontinuous Systems by : Chii-Yuh Chern

Download or read book On Oscillations of Nonlinear Discontinuous Systems written by Chii-Yuh Chern and published by . This book was released on 1971 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bifurcations in Continuous Piecewise Linear Differential Systems

Author : Enrique Ponce
Publisher : Springer Nature
ISBN 13 : 3031211359
Total Pages : 317 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Bifurcations in Continuous Piecewise Linear Differential Systems by : Enrique Ponce

Download or read book Bifurcations in Continuous Piecewise Linear Differential Systems written by Enrique Ponce and published by Springer Nature. This book was released on 2022-12-10 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the qualitative study of differential equations defined by piecewise linear (PWL) vector fields, mainly continuous, and presenting two or three regions of linearity. The study focuses on the more common bifurcations that PWL differential systems can undergo, with emphasis on those leading to limit cycles. Similarities and differences with respect to their smooth counterparts are considered and highlighted. Regarding the dimensionality of the addressed problems, some general results in arbitrary dimensions are included. The manuscript mainly addresses specific aspects in PWL differential systems of dimensions 2 and 3, which are sufficinet for the analysis of basic electronic oscillators. The work is divided into three parts. The first part motivates the study of PWL differential systems as the natural next step towards dynamic complexity when starting from linear differential systems. The nomenclature and some general results for PWL systems in arbitrary dimensions are introduced. In particular, a minimal representation of PWL systems, called canonical form, is presented, as well as the closing equations, which are fundamental tools for the subsequent study of periodic orbits. The second part contains some results on PWL systems in dimension 2, both continuous and discontinuous, and both with two or three regions of linearity. In particular, the focus-center-limit cycle bifurcation and the Hopf-like bifurcation are completely described. The results obtained are then applied to the study of different electronic devices. In the third part, several results on PWL differential systems in dimension 3 are presented. In particular, the focus-center-limit cycle bifurcation is studied in systems with two and three linear regions, in the latter case with symmetry. Finally, the piecewise linear version of the Hopf-pitchfork bifurcation is introduced. The analysis also includes the study of degenerate situations. Again, the above results are applied to the study of different electronic oscillators.

Mathematical Modeling of Discontinuous Processes

Author : Andrey Antonov
Publisher : Scientific Research Publishing, Inc. USA
ISBN 13 : 1618964402
Total Pages : 239 pages
Book Rating : 4.6/5 (189 download)

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Book Synopsis Mathematical Modeling of Discontinuous Processes by : Andrey Antonov

Download or read book Mathematical Modeling of Discontinuous Processes written by Andrey Antonov and published by Scientific Research Publishing, Inc. USA. This book was released on 2017-12-19 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph as a mathematical apparatus are used and investigated several classes of differential equations. The most significant feature of these differential equations is the presence of impulsive effects. The main goals and the results achieved in the monograph are related to the use of this class of equation for an adequate description of the dynamics of several types of processes that are subject to discrete external interventions and change the speed of development. In all proposed models the following requirements have met: 1) Presented and studied mathematical models in the book are extensions of existing known in the literature models of real objects and related processes. 2) Generalizations of the studied models are related to the admission of external impulsive effects, which lead to “jump-like” change the quantity characteristics of the described object as well as the rate of its modification. 3) Sufficient conditions which guarantee certain qualities of the dynamics of the quantities of the modeled objects are found. 4) Studies of the qualities of the modification of the modeled objects are possible to be successful by differential equations with variable structure and impulsive effects. 5) The considerations relating to the existence of the studied properties of dynamic objects cannot be realized without introducing new concepts and proving of appropriate theorems. The main objectives can be conditionally divided into several parts: 1) New classes of differential equations with variable structure and impulses are introduced and studied; 2) Specific properties of the above-mentioned class of differential equations are introduced and studied. The present monograph consists of an introduction and seven chapters. Each chapter contains several sections.

A Smooth and Discontinuous Oscillator

Author : Qingjie Cao
Publisher : Springer
ISBN 13 : 3662530945
Total Pages : 262 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis A Smooth and Discontinuous Oscillator by : Qingjie Cao

Download or read book A Smooth and Discontinuous Oscillator written by Qingjie Cao and published by Springer. This book was released on 2016-09-27 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.