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Dynamics Of Nonlinear Time Delay Systems

Dynamics of Nonlinear Time Delay Systems PDF

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Author: Muthusamy Lakshmanan
Publisher: Springer Science & Business Media
ISBN: 9783642149382
Size: 68.14 MB
Format: PDF
Category : Science
Languages : en
Pages : 313
View: 7643

Book Description: 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.


Sequential Bifurcation Trees To Chaos In Nonlinear Time Delay Systems

Sequential Bifurcation Trees to Chaos in Nonlinear Time Delay Systems PDF

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Author: Siyuan Xing
Publisher: Morgan & Claypool Publishers
ISBN: 1681739437
Size: 20.36 MB
Format: PDF, Mobi
Category : Technology & Engineering
Languages : en
Pages : 87
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Book Description: In this book, the global sequential scenario of bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is presented for a better understanding of global behaviors and motion transitions for one periodic motion to another one. A 1-dimensional (1-D), time-delayed, nonlinear dynamical system is considered as an example to show how to determine the global sequential scenarios of the bifurcation trees of periodic motions to chaos. All stable and unstable periodic motions on the bifurcation trees can be determined. Especially, the unstable periodic motions on the bifurcation trees cannot be achieved from the traditional analytical methods, and such unstable periodic motions and chaos can be obtained through a specific control strategy. The sequential periodic motions in such a 1-D time-delayed system are achieved semi-analytically, and the corresponding stability and bifurcations are determined by eigenvalue analysis. Each bifurcation tree of a specific periodic motion to chaos are presented in detail. The bifurcation tree appearance and vanishing are determined by the saddle-node bifurcation, and the cascaded period-doubled periodic solutions are determined by the period-doubling bifurcation. From finite Fourier series, harmonic amplitude and harmonic phases for periodic motions on the global bifurcation tree are obtained for frequency analysis. Numerical illustrations of periodic motions are given for complex periodic motions in global bifurcation trees. The rich dynamics of the 1-D, delayed, nonlinear dynamical system is presented. Such global sequential periodic motions to chaos exist in nonlinear dynamical systems. The frequency-amplitude analysis can be used for re-construction of analytical expression of periodic motions, which can be used for motion control in dynamical systems.


Dynamical Systems

Dynamical Systems PDF

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Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 9781441957542
Size: 69.30 MB
Format: PDF, ePub, Mobi
Category : Technology & Engineering
Languages : en
Pages : 464
View: 378

Book Description: 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.


Robust Control For Nonlinear Time Delay Systems

Robust Control for Nonlinear Time Delay Systems PDF

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Author: Changchun Hua
Publisher: Springer
ISBN: 9811051313
Size: 59.12 MB
Format: PDF, ePub
Category : Technology & Engineering
Languages : en
Pages : 300
View: 7740

Book Description: This book reports on the latest findings concerning nonlinear control theory and applications. It presents novel work on several kinds of commonly encountered nonlinear time-delay systems, including those whose nonlinear terms satisfy high-order polynomial form or general nonlinear form, those with nonlinear input or a triangular structure, and so on. As such, the book will be of interest to university researchers, R&D engineers and graduate students in the fields of control theory and control engineering who wish to learn about the core principles, methods, algorithms, and applications of nonlinear time-delay systems.


Control Of Complex Nonlinear Systems With Delay

Control of Complex Nonlinear Systems with Delay PDF

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Author: Philipp Hövel
Publisher: Springer Science & Business Media
ISBN: 9783642141102
Size: 73.44 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 253
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Book Description: This research addresses delay effects in nonlinear systems, which are ubiquitous in various fields of physics, chemistry, biology, engineering, and even in social and economic systems. They may arise as a result of processing times or due to the finite propagation speed of information between the constituents of a complex system. Time delay has two complementary, counterintuitive and almost contradictory facets. On the one hand, delay is able to induce instabilities, bifurcations of periodic and more complicated orbits, multi-stability and chaotic motion. On the other hand, it can suppress instabilities, stabilize unstable stationary or periodic states and may control complex chaotic dynamics. This thesis deals with both aspects, and presents novel fundamental results on the controllability of nonlinear dynamics by time-delayed feedback, as well as applications to lasers, hybrid-mechanical systems, and coupled neural systems.


Delay Differential Equations

Delay Differential Equations PDF

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Author: Yang Kuang
Publisher: Academic Press
ISBN: 9780080960029
Size: 70.32 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 398
View: 5003

Book Description: Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems. The book treats both autonomous and nonautonomous systems with various delays. Key topics addressed are the possible delay influence on the dynamics of the system, such as stability switching as time delay increases, the long time coexistence of populations, and the oscillatory aspects of the dynamics. The book also includes coverage of the interplay of spatial diffusion and time delays in some diffusive delay population models. The treatment presented in this monograph will be of great value in the study of various classes of DDEs and their multidisciplinary applications.


Recent Results On Nonlinear Delay Control Systems

Recent Results on Nonlinear Delay Control Systems PDF

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Author: Iasson Karafyllis
Publisher: Springer
ISBN: 331918072X
Size: 21.89 MB
Format: PDF, Mobi
Category : Technology & Engineering
Languages : en
Pages : 407
View: 2483

Book Description: This volume collects recent advances in nonlinear delay systems, with an emphasis on constructive generalized Lyapunov and predictive approaches that certify stability properties. The book is written by experts in the field and includes two chapters by Miroslav Krstic, to whom this volume is dedicated. This volume is suitable for all researchers in mathematics and engineering who deal with nonlinear delay control problems and students who would like to understand the current state of the art in the control of nonlinear delay systems.


Time Delay Systems

Time Delay Systems PDF

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Author: Tamás Insperger
Publisher: Springer
ISBN: 3319534262
Size: 78.60 MB
Format: PDF, ePub
Category : Technology & Engineering
Languages : en
Pages : 362
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Book Description: This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike.


Time Delayed Chaotic Dynamical Systems

Time Delayed Chaotic Dynamical Systems PDF

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Author: Tanmoy Banerjee
Publisher: Springer
ISBN: 3319709933
Size: 26.59 MB
Format: PDF, ePub, Mobi
Category : Technology & Engineering
Languages : en
Pages : 114
View: 4407

Book Description: This book describes systematic design techniques for chaotic and hyperchaotic systems, the transition from one to the other, and their implementation in electronic circuits. It also discusses the collective phenomena manifested by these systems when connected by a physical coupling scheme. Readers will be introduced to collective behaviours, such as synchronization and oscillation suppression, and will learn how to implement nonlinear differential equations in electronic circuits. Further, the book shows how the choice of nonlinearity can lead to chaos and hyperchaos, even in a first-order time-delayed system. The occurrence of these phenomena, together with the efficiency of the design techniques described, is presented with theoretical studies, numerical characterization and experimental demonstrations with the corresponding electronic circuits, helping readers grasp the design aspects of dynamical systems as a whole in electronic circuits. The authors then discuss the usefulness of an active all-pass filter as the delay element, supported by their own experimental observations, as well as theoretical and numerical results. Including detailed analysis, as well as computations with suitable dedicated software packages, the book will be of interest to all academics and researchers who wish to expand their knowledge of the subtlety of nonlinear time-delayed systems. It also offers a valuable source of information for engineers, linking the design techniques of chaotic time-delayed systems with their collective phenomena.