English | 2022 | ISBN: 0750339012, 978-0-7503-3903-2 | 278 pages | True PDF EPUB MOBI | 56.78 MB
The last few years have seen dramatic advances in the growth, fabrication and characterization of low-dimensional materials (such as graphene) and nanostructures (such as those formed from ultrathin films, wires, discs and other "dots"), formed either singly or in spatially periodic arrays. Most studies of these artificially engineered materials have been driven by their potential for device applications that involve smaller and smaller physical dimensions. In particular, the dynamical properties of these materials are of fundamental interest for the devices that involve high-frequency operation and/or switching. Consequently, the different excitations, vibrational, magnetic, optical, electronic, and so on, need to be understood from the perspective of how their properties are modified in finite structures especially on the nanometre length scale due to the presence of surfaces and interfaces. Recently, the patterning of nanoelements, into periodic and other arrays, has become a focus of intense activity, leading for example to photonic crystals and their analogues such as phononic and magnonic crystals where the control of the band gaps in the excitation spectrum is a basis for applications. The nonlinear properties of the excitations are increasingly a topic of interest, as well as the linear dynamics.
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English | 2021 | ISBN: 147045114X, 978-1470465407 | 553 pages | True PDF | 7.76 MB
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time―pure and applied alike―ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.

English | 2022 | ISBN: 3030903427 | 250 pages | True PDF EPUB | 48.62 MB
This book describes a user-friendly, evolutionary algorithms-based framework for estimating data-driven models for a wide class of dynamical systems, including linear and nonlinear ones. The methodology addresses the problem of automating the process of estimating data-driven models from a user's perspective. By combining elementary building blocks, it learns the dynamic relations governing the system from data, giving model estimates with various trade-offs, e.g. between complexity and accuracy. The evaluation of the method on a set of academic, benchmark and real-word problems is reported in detail. Overall, the book offers a state-of-the-art review on the problem of nonlinear model estimation and automated model selection for dynamical systems, reporting on a significant scientific advance that will pave the way to increasing automation in system identification.

Dimension Groups and Dynamical Systems
pdf | 6.26 MB | English | Isbn:‎ B09NRP3CR2 | Author: Dominique Perrin | Year: 2022

Introduction To The Modern Theory Of Dynamical Systems Encyclopedia Of Mathematics And Its Applications
pdf | 63.61 MB | English | Isbn:‎ 978-0521575577 | Author: Anatole Katok | Year: 1996

Perspectives in Dynamical Systems I: Mechatronics and Life Sciences
English | 2022 | ISBN: 3030773051 | 260 Pages | PDF EPUB | 63 MB
This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference "Dynamical Systems: Theory and Applications", held in Łódź, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems.

English | 2021 | ISBN: 1636392199 , 978-1636392196 | 167 pages | True PDF | 6.99 MB
The book is about the global stability and bifurcation of equilibriums in polynomial functional systems.Appearing and switching bifurcations of simple and higher-order equilibriums in the polynomial functional systems are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The third-order sink and source bifurcations for simple equilibriums are presented in the polynomial functional systems. The third-order sink and source switching bifurcations for saddle and nodes are also presented, and the fourth-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for two second-order upper-saddles and two second-order lower-saddles, respectively. In general, the (2

Impulsive Synchronization of Complex Dynamical Networks: Modeling, Control and Simulations
English | 2022 | ISBN: 9811653828 | 192 Pages | PDF | 10 MB
This book is mainly focused on the global impulsive synchronization of complex dynamical networks with different types of couplings, such as general state coupling, nonlinear state coupling, time-varying delay coupling, derivative state coupling, proportional delay coupling and distributed delay coupling. Studies on impulsive synchronization of complex dynamical networks have attracted engineers and scientists from various disciplines, such as electrical engineering, mechanical engineering, mathematics, network science, system engineering. Pursuing a holistic approach, the book establishes a fundamental framework for this topic, while emphasizing the importance of network synchronization and the significant influence of impulsive control in the design and optimization of complex networks. The primary audience for the book would be the scholars and graduate students whose research topics including the network science, control theory, applied mathematics, system science and so on.

English | 2021 | ISBN: 0367487322 | 218 pages | pdf | 13.3 MB
Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media.

Model Reduction of Complex Dynamical Systems
English | 2021 | ISBN: 3030729826 | 416 Pages | PDF EPUB | 77 MB
This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems - MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: