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The main purpose of this lecture is to clarify the complex system with that of contradictory system and its importance to the reality of a thing T by extending Banach or Hilbert spaces to Banach or Hilbert continuity flow spaces over topological graphs and establishing the global differential theory on complex flows.
This work tackles the problems of understanding how energy is transmitted and distributed in power-grids as well as in determining how robust this transmission and distribution is when modifications to the grid or power occur. The most important outcome is the derivation of explicit relationships between the structure of the grid, the optimal transmission and distribution of energy, and the grid’s collective behavior (namely, the synchronous generation of power). These relationships are extremely relevant for the design of resilient power-grid models. To allow the reader to apply these results to other complex systems, the thesis includes a review of relevant aspects of network theory, spectral theory, and novel analytical calculations to predict the existence and stability of periodic collective behavior in complex networks of phase oscillators, which constitute a paradigmatic model for many complex systems.
The origin of the word synchronization is a greek root, meaning "to share the common time". The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the earlier days of physics. Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest.The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled chaotic systems.Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony means in all particular contexts in which we will describe its emergence.The book describes the complete synchronization phenomenon, both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos.Furthermore, the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization, describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators.These concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of all possible situations that are encountered in real life and in technology. - Technical, but not specialistic language - About 100 illustrative Figures - Full overview on synchronization phenomena - Review of the main tools and techniques used in the field - Paradigmatic examples and experiments illustrating the basic concepts - Full Reference to the main publications existing in the literature on the subject
A thing is complex, and hybrid with other things sometimes. Then, what is the reality of a thing? The reality of a thing is its state of existed, exists, or will exist in the world, independent on the understanding of human beings, which implies that the reality holds on by human beings maybe local or gradual, not the reality of a thing. Hence, to hold on the reality of things is the main objective of science in the history of human development.
A hands-on approach to understanding, designing, analyzing, and evaluating complex systems During the last few years, Simulation-Based Systems Engineering (SBSE) has become an essential tool for the design and evaluation of complex systems. This is the first book to cover the basic principles of complex systems through the use of hands-on experimentation using an icon-based simulation tool. Utilizing the accompanying software tool ExtendSim, which works with the OpEMCSS library, readers are invited to engage in simulation-based experiments that demonstrate the principles of complex systems with an emphasis on design, analysis, and evaluation. A number of real-world examples are included to demonstrate how to model complex systems across a range of engineering, business, societal, economic, and scientific disciplines. Beginning with an introduction to SBSE, the book covers: Simulation concepts and building blocks Systems design and model development Markov model development Reliability processes Queuing theory in SBSE Rule-based learning and adaptation Agent motion and spatial interactions Multi-agent system of systems Assuming only a very basic background in problem-solving ability, this book is ideal as a textbook for students (a homework solution manual is also available) and as a reference book for practitioners in industry.
International J. Mathematical Combinatorics is a fully refereed international journal. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces; Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathematical theory on parallel universes; Other applications of Smarandache multi-space and combinatorics.
The Mathematical Combinatorics (International Book Series) is a fully refereed international book series with ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 110-160 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences.
"This chapter offers some historical and conceptual orientation to readers of the Oxford Handbook of Entertainment Theory. Departing from a brief review of ancient roots and 20th century pioneer works, we elaborate on the state and challenges of contemporary entertainment theory and research. This includes the need to develop a more explicit understanding of interrelationships among similar terms and concepts (e.g., presence and transportation), the need to reflect more explicitly on epistemological foundations of entertaiment theories (e.g., neo-behaviorism), and the need to reach back to past, even historical reasoning in communication that may be just as informative as the consideration of recent theoretical innovations from neigboring fields such as social psychology. Finally, we offer some reflections on programmatic perspectives for future entertainment theory, which should try to harmonize views from the social sciences and critical thinking, span cultural differences in entertainment processes, and keep track of the rapid technological progress of entertainment media"--
In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.
This book builds on the cutting edge research presented in the previous edition that was the first of its kind to present the technology behind an emerging power systems management tool still in the early stages of commercial roll-out. In the intervening years, synchrophasors have become a crucial and widely adopted tool in the battle against electricity grid failures around the world. Still the most accurate wide area measurement (WAMS) technology for power systems, synchronized phasor measurements have become increasingly sophisticated and useful for system monitoring, as the advent of big data storage allows for more nuanced real-time analysis, allowing operators to predict, prevent and mitigate the impacts of blackouts with enhanced accuracy and effectiveness. This new edition continues to provide the most encompassing overview of the technology from its pioneers, and has been expanded and updated to include all the applications and optimizations of the last decade.