Dynamics Of Nonlinear Systems
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Nonlinear Dynamical Control Systems
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Author : Henk Nijmeijer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nonlinear Dynamical Control Systems written by Henk Nijmeijer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Technology & Engineering categories.
This book has recently been retypeset in LaTeX for clearer presentation. This textbook on the differential geometric approach to nonlinear control grew out of a set of lecture notes, which were prepared for a course on nonlinear system theory, given by us for the first time during the fall semester of 1988. The audience consisted mostly of graduate students , taking part in the Dutch national Graduate Program on Systems and Control.The course gives a general introduction to modern nonlinear control theory (with an emphasis on the differential geometric approach), as well as providing students specializing in nonlinear control theory with a firm starting point for doing research in this area. One of the authors' primary objectives is to give a self-contained treatment of all the topics covered. Although the amount of work published on nonlinear geometric control theory is expanding rapidly expanding, the authors confine themselves to treating solid and clear-cut achievements of modern nonlinear control, which can be expected to be of remaining interest. The final selection of topics reflects the authors' own judgement of their importance.
Dynamics Of Nonlinear Time Delay Systems
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Author : Muthusamy Lakshmanan
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-04
Dynamics Of Nonlinear Time Delay Systems written by Muthusamy Lakshmanan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-04 with Science categories.
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions. Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.
Chaotic Dynamics Of Nonlinear Systems
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Author : S. Neil Rasband
language : en
Publisher: Courier Dover Publications
Release Date : 2015-08-19
Chaotic Dynamics Of Nonlinear Systems written by S. Neil Rasband and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Science categories.
Introduction to the concepts, applications, theory, and technique of chaos. Suitable for advanced undergraduates and graduate students and researchers. Requires familiarity with differential equations and linear vector spaces. 1990 edition.
Nonlinear System Dynamics
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Author : W. Richard Kolk
language : en
Publisher: Springer
Release Date : 1992-01-31
Nonlinear System Dynamics written by W. Richard Kolk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-31 with Science categories.
Engineers, scientists, and applied mathematicians are habitually curious about behavior of physical systems. More often than not they will model the system and then analyze the model, hoping to expose the system's dynamic secrets. Traditionally, linear methods have been the norm and nonlinear effects were only added peripherally. This bias for linear techniques arises from the consum mate beauty and order in linear subs paces and the elegance of linear indepen dence is too compelling to be denied. And the bias has been, in the past, for tified by the dearth of nonlinear procedures, rendering the study of nonlinear dynamics untidy. But now a new attractiveness is being conferred on that non descript patchwork, and the virtue of the hidden surprises is gaining deserved respect. With a wide variety of individual techniques available, the student and the engineer as well as the scientist and researcher, are faced with an almost overwhelming task of which to use to help achieve an understanding sufficient to reach a satisfying result. If linear analysis predicts system behavior suffi ciently close to reality, that is delightful. In the more likely case where nonlin ear analysis is required, we believe this text fills an important void. We have tried to compile and bring some order to a large amount of information and techniques, that although well known, is scattered. We have also extended this knowledge base with new material not previously published.
Nonlinear Dynamics And Statistics
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Author : Alistair I. Mees
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Dynamics And Statistics written by Alistair I. Mees and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
All models are lies. "The Earth orbits the sun in an ellipse with the sun at one focus" is false, but accurate enough for almost all purposes. This book describes the current state of the art of telling useful lies about time-varying systems in the real world. Specifically, it is about trying to "understand" (that is, tell useful lies about) dynamical systems directly from observa tions, either because they are too complex to model in the conventional way or because they are simply ill-understood. B(:cause it overlaps with conventional time-series analysis, building mod els of nonlinear dynamical systems directly from data has been seen by some observers as a somewhat ill-informed attempt to reinvent time-series analysis. The truth is distinctly less trivial. It is surely impossible, except in a few special cases, to re-create Newton's astonishing feat of writing a short equation that is an excellent description of real-world phenomena. Real systems are connected to the rest of the world; they are noisy, non stationary, and have high-dimensional dynamics; even when the dynamics contains lower-dimensional attractors there is almost never a coordinate system available in which these at tractors have a conventionally simple description.
Bifurcation And Stability In Nonlinear Dynamical Systems
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2020-01-30
Bifurcation And Stability In Nonlinear Dynamical Systems written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Mathematics categories.
This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems. From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will bring us to the new era of dynamical systems and control. Presents an efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums; Discusses dynamics of infinite-equilibrium systems; Demonstrates higher-order singularity.
Nonlinear Control Systems And Power System Dynamics
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Author : Qiang Lu
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03-31
Nonlinear Control Systems And Power System Dynamics written by Qiang Lu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-31 with Mathematics categories.
Nonlinear Control Systems and Power System Dynamics presents a comprehensive description of nonlinear control of electric power systems using nonlinear control theory, which is developed by the differential geometric approach and nonlinear robust control method. This book explains in detail the concepts, theorems and algorithms in nonlinear control theory, illustrated by step-by-step examples. In addition, all the mathematical formulation involved in deriving the nonlinear control laws of power systems are sufficiently presented. Considerations and cautions involved in applying nonlinear control theory to practical engineering control designs are discussed and special attention is given to the implementation of nonlinear control laws using microprocessors. Nonlinear Control Systems and Power System Dynamics serves as a text for advanced level courses and is an excellent reference for engineers and researchers who are interested in the application of modern nonlinear control theory to practical engineering control designs.
Nonlinear Dynamical Systems And Control
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Author : Wassim M. Haddad
language : en
Publisher: Princeton University Press
Release Date : 2011-09-19
Nonlinear Dynamical Systems And Control written by Wassim M. Haddad and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-19 with Mathematics categories.
Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.
Applications Of Nonlinear Dynamics
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Author : Visarath In
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Applications Of Nonlinear Dynamics written by Visarath In and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-11 with Technology & Engineering categories.
The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.
Nonlinear Dynamics And Chaos
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Author : Steven H. Strogatz
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Dynamics And Chaos written by Steven H. Strogatz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.