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Mathematical physics --- Engineering sciences. Technology --- Computer science --- theoretische fysica --- ingenieurswetenschappen

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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.  This book also:  Presents novel concepts and methods for dynamical system synchronization Extends beyond the Lyapunov theory for dynamical system synchronization Introduces companion and synchronization of discrete dynamical systems Includes local singularity theory for discontinuous dynamical systems Covers the invariant domains of synchronization Features more than 75 illustrations Dynamical System Synchronization is an ideal book for those interested in better understanding new concepts and methodology for dynamical system synchronization, local singularity theory for discontinuous dynamical systems, distinct dynamical system synchronization, and invariant domains of synchronization.

Differential geometry. Global analysis --- Ergodic theory. Information theory --- Physics --- Applied physical engineering --- Computer science --- differentiaal geometrie --- informatica --- ingenieurswetenschappen --- fysica --- informatietheorie

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This book for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems. Facilitates discovery of analytical solutions of nonlinear time-delay systems; Illustrates bifurcation trees of periodic motions to chaos; Helps readers identify motion complexity and singularity; Explains procedures for determining stability, bifurcation and chaos.

Discrete mathematics --- Classical mechanics. Field theory --- Statistical physics --- Applied physical engineering --- Computer science --- chaos --- toegepaste wiskunde --- grafentheorie --- theoretische fysica --- time series analysis --- informatica --- ingenieurswetenschappen --- dynamica

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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. This volume also: Discusses discontinuous dynamical systems as applied to real-world issues, like the behavior of suspension systems in railways, the multifractal spectrum of LAN traffic and their correlations, as well as the effect of nonlinear vibration and applied control on coal manufacturing. Includes material on time-delay systems as they relate to linear switching systems, dynamics of complex networks and machine tools with multiple boundaries. Presents numerous theories and aspects of vibration and control, using worked mathematical examples and empirical evidence to argue the pros and cons of all theories. Dynamical Systems: Discontinuous, Stochasticity and Time-Delay is the ideal book for engineers and academic researchers working in areas like mechanical and control engineering, as well as applied mathematics.

Mathematics --- Classical mechanics. Field theory --- Mechanical properties of solids --- Electrical engineering --- Applied physical engineering --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- patroonherkenning --- mechatronica --- superclaus proces --- industriële robots --- automatisering --- systeemtheorie --- systeembeheer --- ingenieurswetenschappen --- robots --- dynamica --- automatische regeltechniek --- optica

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This book focuses on bifurcation and stability in nonlinear discrete systems, including monotonic and oscillatory stability. It presents the local monotonic and oscillatory stability and bifurcation of period-1 fixed-points on a specific eigenvector direction, and discusses the corresponding higher-order singularity of fixed-points. Further, it explores the global analysis of monotonic and oscillatory stability of fixed-points in 1-dimensional discrete systems through 1-dimensional polynomial discrete systems. Based on the Yin-Yang theory of nonlinear discrete systems, the book also addresses the dynamics of forward and backward nonlinear discrete systems, and the existence conditions of fixed-points in said systems. Lastly, in the context of local analysis, it describes the normal forms of nonlinear discrete systems and infinite-fixed-point discrete systems. Examining nonlinear discrete systems from various perspectives, the book helps readers gain a better understanding of the nonlinear dynamics of such systems.

Ergodic theory. Information theory --- Mathematics --- Classical mechanics. Field theory --- Mechanical properties of solids --- Electrical engineering --- Computer. Automation --- patroonherkenning --- complexiteit --- wiskunde --- dynamica --- automatische regeltechniek --- optica