Principles Of Discontinuous Dynamical Systems

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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.

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.

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.

Discontinuous Dynamical Systems on Time-varying Domains

Author : Albert Luo
Publisher : Springer
ISBN 13 : 9783642010262
Total Pages : 228 pages
Book Rating : 4.0/5 (12 download)

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

Download or read book Discontinuous Dynamical Systems on Time-varying Domains written by Albert Luo and published by Springer. This book was released on 2010-05-06 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.

Regularity and Complexity in Dynamical Systems

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 1461415233
Total Pages : 500 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Regularity and Complexity in Dynamical Systems by : Albert C. J. Luo

Download or read book Regularity and Complexity in Dynamical Systems written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2013-07-12 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

System Dynamics with Interaction Discontinuity

Author : Albert C. J. Luo
Publisher : Springer
ISBN 13 : 3319174223
Total Pages : 257 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis System Dynamics with Interaction Discontinuity by : Albert C. J. Luo

Download or read book System Dynamics with Interaction Discontinuity written by Albert C. J. Luo and published by Springer. This book was released on 2015-07-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

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.

Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities

Author : Marat Akhmet
Publisher : Springer
ISBN 13 : 9811031800
Total Pages : 166 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities by : Marat Akhmet

Download or read book Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities written by Marat Akhmet and published by Springer. This book was released on 2017-01-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.

Dynamical Systems

Author : Albert C.J. Luo
Publisher : Springer
ISBN 13 : 9781441957535
Total Pages : 464 pages
Book Rating : 4.9/5 (575 download)

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

Download or read book Dynamical Systems written by Albert C.J. Luo and published by Springer. This book was released on 2010-06-10 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical Systems: Discontinuous, Stochasticity and Time-Delay provides an overview of the most recent developments in nonlinear dynamics, vibration and control. This book focuses on the most recent advances in all three areas, with particular emphasis on recent analytical, numerical and experimental research and its results. Real dynamical system problems, such as the behavior of suspension systems of railways, nonlinear vibration and applied control in coal manufacturing, along with the multifractal spectrum of LAN traffic, are discussed at length, giving the reader a sense of real-world instances where these theories are applied. Dynamical Systems: Discontinuous, Stochasticity and Time-Delay also contains material on time-delay systems as they relate to linear switching, dynamics of complex networks, and machine tools with multiple boundaries. It is the ideal book for engineers and academic researchers working in areas like mechanical and control engineering, as well as applied mathematics.

Regularity and Stochasticity of Nonlinear Dynamical Systems

Author : Dimitri Volchenkov
Publisher : Springer
ISBN 13 : 3319580620
Total Pages : 311 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Regularity and Stochasticity of Nonlinear Dynamical Systems by : Dimitri Volchenkov

Download or read book Regularity and Stochasticity of Nonlinear Dynamical Systems written by Dimitri Volchenkov and published by Springer. This book was released on 2017-06-24 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

Journal of Dynamic Systems, Measurement, and Control

Author :
Publisher :
ISBN 13 :
Total Pages : 542 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Journal of Dynamic Systems, Measurement, and Control by :

Download or read book Journal of Dynamic Systems, Measurement, and Control written by and published by . This book was released on 2005 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamical System Synchronization

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 1461450977
Total Pages : 245 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Dynamical System Synchronization by : Albert C. J. Luo

Download or read book Dynamical System Synchronization written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2013-03-22 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques.

System Modeling and Optimization

Author : Dietmar Hömberg
Publisher : Springer
ISBN 13 : 3642360629
Total Pages : 568 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis System Modeling and Optimization by : Dietmar Hömberg

Download or read book System Modeling and Optimization written by Dietmar Hömberg and published by Springer. This book was released on 2013-02-20 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of thoroughly refereed papers presented at the 25th IFIP TC 7 Conference on System Modeling and Optimization, held in Dresden, Germany, in September 2011. The 55 revised papers were carefully selected from numerous submissions. They are organized in the following topical sections: control of distributed parameter systems; stochastic optimization and control; stabilization, feedback, and model predictive control; flow control; shape and structural optimization; and applications and control of lumped parameter systems.

Stability of Dynamical Systems

Author : Anthony N. Michel
Publisher : Springer
ISBN 13 : 3319152750
Total Pages : 653 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Stability of Dynamical Systems by : Anthony N. Michel

Download or read book Stability of Dynamical Systems written by Anthony N. Michel and published by Springer. This book was released on 2015-03-30 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems. For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonic Lyapunov functions. Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks. The authors cover 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 involving monotonic and non-monotonic Lyapunov functions - Specialization of this stability theory to finite-dimensional dynamical systems - Specialization of this stability theory to infinite-dimensional dynamical systems Replete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this book can be used as a textbook for graduate courses in stability theory of dynamical systems. It may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, economics, and the physical and life sciences. Review of the First Edition: “The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems. [This] is a very interesting book which complements the existing literature. [It] is clearly written, and difficult concepts are illustrated by means of good examples.” - Alessandro Astolfi, IEEE Control Systems Magazine, February 2009

Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions

Author : Yury Orlov
Publisher : Springer Nature
ISBN 13 : 3030376257
Total Pages : 351 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions by : Yury Orlov

Download or read book Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions written by Yury Orlov and published by Springer Nature. This book was released on 2020-02-08 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous systems—those with variable structure and impact—by the involvement of nonsmooth Lyapunov functions. The general theoretical presentation is illustrated by control-related applications; the nonsmooth Lyapunov construction is particularly applied to the tuning of sliding-mode controllers in the presence of mismatched disturbances and to orbital stabilization of the bipedal gate. The nonsmooth construction is readily extendible to the control and identification of distributed-parameter and time-delay systems. The first part of the book outlines the relevant fundamentals of benchmark models and mathematical basics. The second concentrates on the construction of nonsmooth Lyapunov functions. Part III covers design and applications material. This book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems. It will also serve the practitioner working with applications of such systems. The reader should have some knowledge of dynamical systems theory, but no background in discontinuous systems is required—they are thoroughly introduced in both finite- and infinite-dimensional settings.

Neural Networks with Discontinuous/Impact Activations

Author : Marat Akhmet
Publisher : Springer Science & Business Media
ISBN 13 : 1461485665
Total Pages : 168 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Neural Networks with Discontinuous/Impact Activations by : Marat Akhmet

Download or read book Neural Networks with Discontinuous/Impact Activations written by Marat Akhmet and published by Springer Science & Business Media. This book was released on 2013-10-30 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided.