Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.

Discrete mathematics --- Computer. Automation --- grafentheorie --- complexiteit --- systeemtheorie

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is useful to engineers, researchers, entrepreneurs, and students in different branches of production, engineering, and systems sciences. The polytopic roadmaps are the guidelines inspired by the development stages of cognitive-intelligent systems, and expected to become powerful instruments releasing an abundance of new capabilities and structures for complex engineering systems implementation. The 4D approach developed in previous monographs and correlated with industry 4.0and Fourth Industrial Revolution is continued here toward higher dimensions approaches correlated with polytopic operations, equipment, technologies, industries, and societies. Methodology emphasizes the role of doubling, iteration, dimensionality, and cyclicality around the center, of periodic tables and of conservative and exploratory strategies. Partitions, permutations, classifications, and complexification, as polytopic chemistry, are the elementary operations analyzed. Multi-scale transfer, cyclic operations, conveyors, and assembly lines are the practical examples of operations and equipment. Polytopic flow sheets, online analytical processing, polytopic engineering designs, and reality-inspired engineering are presented. Innovative concepts such as Industry 5.0, polytopic industry, Society 5.0, polytopic society, cyber physical social systems, industrial Internet, and digital twins have been discussed. The general polytopic roadmaps, (GPTR), are proposed as universal guidelines and as common methodologies to synthesize the systemic thinking and capabilities for growing complexity projects implementation. .

Discrete mathematics --- Mathematics --- Classical mechanics. Field theory --- grafentheorie --- systeemtheorie --- dynamica

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This text addresses systems with persistent memory that are common mathematical models used in the study of viscoelasticity and thermodynamics with memory. In particular, this class of systems is used to model non-Fickian diffusion in the presence of complex molecular structures. Hence, it has wide applications in biology. The book focuses on the properties and controllability of the archetypal heat and wave equations with memory and introduces the dynamic approach to identification problems and the basic techniques used in the study of stability. The book presents several approaches currently used to study systems with persistent memory: Volterra equation in Hilbert spaces, Laplace transform techniques and semigroup methods. The text is intended for a diverse audience in applied mathematics and engineering and it can be used in PhD courses. Readers are recommended to have a background in the elements of functional analysis. Topics of functional analysis which younger readers may need to familiarize with are presented in the book.

Functional analysis --- Discrete mathematics --- grafentheorie --- functies (wiskunde) --- systeemtheorie

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book explores Complex System Governance (CSG)-an emerging field concerned with the design, execution, and evolution of essential functions necessary to ensure continued viability of a system. The book focuses on three primary development areas to better understand and utilize current developments CSG. First, the conceptual foundations for CSG are developed, from systems theory, management cybernetics, and governance. Second, a set of critical CSG topics are examined from conceptual as well as practice perspectives. Third, several development and application issues are discussed. Ultimately, CSG is positioned as an emerging field with strong theoretical grounding and significant implications for improving practices and performance to better address complex systems and their problems.

Statistical science --- Discrete mathematics --- Computer. Automation --- grafentheorie --- computers --- statistiek --- systeemtheorie

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Discrete mathematics --- Electrical engineering --- grafentheorie --- systeemtheorie --- elektrische circuits