Nonlinear Dynamical Systems

Author : George Datseris,Ulrich Parlitz
Publisher : Springer Nature
Page : 243 pages
File Size : 40,6 Mb
Release : 2022-03-13
Category : Science
ISBN : 9783030910327

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Nonlinear Dynamics by George Datseris,Ulrich Parlitz Pdf

This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 51,9 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

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.

Author : Vasile Marinca,Nicolae Herisanu
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 45,5 Mb
Release : 2012-01-05
Category : Technology & Engineering
ISBN : 9783642227356

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Nonlinear Dynamical Systems in Engineering by Vasile Marinca,Nicolae Herisanu Pdf

This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

Author : Maria Tomas-Rodriguez,Stephen P. Banks
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 44,7 Mb
Release : 2010-02-04
Category : Mathematics
ISBN : 9781849961004

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Linear, Time-varying Approximations to Nonlinear Dynamical Systems by Maria Tomas-Rodriguez,Stephen P. Banks Pdf

Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

Author : Jan A. Sanders,Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 53,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475745757

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Averaging Methods in Nonlinear Dynamical Systems by Jan A. Sanders,Ferdinand Verhulst Pdf

In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.

Author : H.G Solari
Publisher : Routledge
Page : 369 pages
File Size : 43,7 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351428309

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Nonlinear Dynamics by H.G Solari Pdf

Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,8 Mb
Release : 2024-06-16
Category : Electronic
ISBN : 9789814462716

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Nonlinear Dynamical Systems of Mathematical Physics by Anonim Pdf

Author : Jan H. Richter
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 43,5 Mb
Release : 2011-01-16
Category : Technology & Engineering
ISBN : 9783642176272

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Reconfigurable Control of Nonlinear Dynamical Systems by Jan H. Richter Pdf

This research monograph summarizes solutions to reconfigurable fault-tolerant control problems for nonlinear dynamical systems that are based on the fault-hiding principle. It emphasizes but is not limited to complete actuator and sensor failures. In the first part, the monograph starts with a broad introduction of the control reconfiguration problems and objectives as well as summaries and explanations of solutions for linear dynamical systems. The solution is always a reconfiguration block, which consists of linear virtual actuators in the case of actuator faults and linear virtual sensors in the case of sensor faults. The main advantage of the fault-hiding concept is the reusability of the nominal controller, which remains in the loop as an active system while the virtual actuator and sensor adapt the control input and the measured output to the fault scenario. The second and third parts extend virtual actuators and virtual sensors towards the classes of Hammerstein-Wiener systems and piecewise affine systems. The main analyses concern stability recovery, setpoint tracking recovery, and performance recovery as reconfiguration objectives. The fourth part concludes the monograph with descriptions of practical implementations and case studies. The book is primarily intended for active researchers and practicing engineers in the field of fault-tolerant control. Due to many running examples it is also suitable for interested graduate students.

Author : Wassim M. Haddad,VijaySekhar Chellaboina
Publisher : Princeton University Press
Page : 975 pages
File Size : 51,9 Mb
Release : 2011-09-19
Category : Mathematics
ISBN : 9781400841042

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Nonlinear Dynamical Systems and Control by Wassim M. Haddad,VijaySekhar Chellaboina Pdf

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.

Author : Henk Nijmeijer,Arjan van der Schaft
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 50,8 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9781475721010

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Nonlinear Dynamical Control Systems by Henk Nijmeijer,Arjan van der Schaft Pdf

This volume deals with controllability and observability properties of nonlinear systems, as well as various ways to obtain input-output representations. The emphasis is on fundamental notions as (controlled) invariant distributions and submanifolds, together with algorithms to compute the required feedbacks.

Author : Marc R Roussel
Publisher : Morgan & Claypool Publishers
Page : 190 pages
File Size : 42,7 Mb
Release : 2019-05-01
Category : Science
ISBN : 9781643274645

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Nonlinear Dynamics by Marc R Roussel Pdf

This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.

Author : Daniel Kaplan,Leon Glass
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208235

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Understanding Nonlinear Dynamics by Daniel Kaplan,Leon Glass Pdf

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 844 pages
File Size : 50,7 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387217499

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Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins Pdf

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik

Author : Andrei N. Leznov,Mikhail V. Saveliev
Publisher : Birkhäuser
Page : 308 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886383

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Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems by Andrei N. Leznov,Mikhail V. Saveliev Pdf

The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view.

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642971495

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Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst Pdf

Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.