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The Transition to Chaos
Based on courses given at the universities of Texas in Austin, and California in San Diego, this book treats an active fields of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; it continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and it concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature. Problems at the ends of chapters help students clarify their understanding. In this new edition, the presentation will be brought up to date throughout, and a new chapter on open quantum systems will be added.
Fractal Functions, Dimensions and Signal Analysis
This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the count...
Self-Evolvable Systems
This monograph presents key method to successfully manage the growing complexity of systems where conventional engineering and scientific methodologies and technologies based on learning and adaptability come to their limits and new ways are nowadays required. The transition from adaptable to evolvable and finally to self-evolvable systems is highlighted, self-properties such as self-organization, self-configuration, and self-repairing are introduced and challenges and limitations of the self-evolvable engineering systems are evaluated.
Energy Policy Modeling in the 21st Century
The roles and applications of various modeling approaches, aimed at improving the usefulness of energy policy models in public decision making, are covered by this book. The development, validation, and applications of system dynamics and agent-based models in service of energy policy design and assessment in the 21st century is a key focus. A number of modeling approaches and models for energy policy, with a particular focus on low-carbon economic development of regions and states are covered. Chapters on system dynamics methodology, model-based theory, fuzzy system dynamics frame-work, and optimization modeling approach are presented, along with several chapters on future research opportun...
Chaos Theory in Politics
The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.
Nonlinear Systems, Vol. 1
This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.
Managing Complex Tasks with Systems Thinking
This book is about improving human decision making and performance in complex tasks. Utilizing systems thinking approach, this book presents innovative and insightful solutions to various managerial issues in various domains including agriculture, education, climate change, digital transformation, health care, supply chains, and sustainability. Practical insights and operational causal models are systematically presented. The key features of the didactic approach of this book are core knowledge, numerous tables and figures throughout the text, system archetypes, and causal loop models. This book serves as a text for college and university courses on Systems Thinking for Management Decision Making in Complex Tasks. Researchers use the developed “causal models” to design and evaluate various decision-aiding technologies. It is used as a source of practical information for a broad community of decision-makers, researchers, and practitioners concerned with the issue of improving human performance in complex organizational tasks.
Multistability in Physical and Living Systems
This book starts with an introduction to the basic concepts of multistability, then illustrates how multistability arises in different systems and explains the main mechanisms of multistability emergence. A special attention is given to noise which can convert a multistable deterministic system to a monostable stochastic one. Furthermore, the most important applications of multistability in different areas of science, engineering and technology are given attention throughout the book, including electronic circuits, lasers, secure communication, and human perception. The book aims to provide a first approach to multistability for readers, who are interested in understanding its fundamental co...
Polystochastic Models for Complexity
This book is devoted to complexity understanding and management, considered as the main source of efficiency and prosperity for the next decades. Divided into six chapters, the book begins with a presentation of basic concepts as complexity, emergence and closure. The second chapter looks to methods and introduces polystochastic models, the wave equation, possibilities and entropy. The third chapter focusing on physical and chemical systems analyzes flow-sheet synthesis, cyclic operations of separation, drug delivery systems and entropy production. Biomimetic systems represent the main objective of the fourth chapter. Case studies refer to bio-inspired calculation methods, to the role of art...
Synchronization of Integral and Fractional Order Chaotic Systems
This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected exp...
