This encyclopedia provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. It links fundamental concepts of mathematics and computational sciences to applications in the physical sciences, engineering, biomedicine, economics and the social sciences.

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

This pioneering text provides a comprehensive introduction to systems structure, function, and modeling as applied in all fields of science and engineering. Systems understanding is increasingly recognized as a key to a more holistic education and greater problem solving skills, and is also reflected in the trend toward interdisciplinary approaches to research on complex phenomena. While the concepts and components of systems science will continue to be distributed throughout the various disciplines, undergraduate degree programs in systems science are also being developed, including at the authors’ own institutions. However, the subject is approached, systems science as a basis for understanding the components and drivers of phenomena at all scales should be viewed with the same importance as a traditional liberal arts education. Principles of Systems Science contains many graphs, illustrations, side bars, examples, and problems to enhance understanding. From basic principles of organization, complexity, abstract representations, and behavior (dynamics) to deeper aspects such as the relations between information, knowledge, computation, and system control, to higher order aspects such as auto-organization, emergence and evolution, the book provides an integrated perspective on the comprehensive nature of systems. It ends with practical aspects such as systems analysis, computer modeling, and systems engineering that demonstrate how the knowledge of systems can be used to solve problems in the real world. Each chapter is broken into parts beginning with qualitative descriptions that stand alone for students who have taken intermediate algebra. The second part presents quantitative descriptions that are based on pre-calculus and advanced algebra, providing a more formal treatment for students who have the necessary mathematical background. Numerous examples of systems from every realm of life, including the physical and biological sciences, humanities, social sciences, engineering, pre-med and pre-law, are based on the fundamental systems concepts of boundaries, components as subsystems, processes as flows of materials, energy, and messages, work accomplished, functions performed, hierarchical structures, and more. Understanding these basics enables further understanding both of how systems endure and how they may become increasingly complex and exhibit new properties or characteristics. Serves as a textbook for teaching systems fundamentals in any discipline or for use in an introductory course in systems science degree programs Addresses a wide range of audiences with different levels of mathematical sophistication Includes open-ended questions in special boxes intended to stimulate integrated thinking and class discussion Describes numerous examples of systems in science and society Captures the trend towards interdisciplinary research and problem solving

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, combines the main features of Game Theory, covering most of the fundamental theoretical aspects under the cooperative and non-cooperative approaches, with the procedures of Agent-Based Modeling for studying complex systems composed of a large number of interacting entities with many degrees of freedom. In Game Theory, the cooperative approach focuses on the possible outcomes of the decision-makers’ interaction by abstracting from the "rational" actions or decisions that may lead to these outcomes. The non-cooperative approach focuses on the actions that the decision-makers can take. As John von Neumann and Oskar Morgenstern argued in their path-breaking book of 1944 entitled Theory of Games and Economic Behavior, most economic questions should be analyzed as games. The models of game theory are abstract representations of a number of real-life situations and have applications to economics, political science, computer science, evolutionary biology, social psychology, and law among others. Agent-Based Modeling (ABM) is a relatively new computational modeling paradigm which aims to construct the computational counterpart of a conceptual model of the system under study on the basis of discrete entities (i.e., the agent) with some properties and behavioral rules, and then to simulate them in a computer to mimic the real phenomena. Given the relative immaturity of this modeling paradigm, and the broad spectrum of disciplines in which it is applied, a clear cut and widely accepted definition of high level concepts of agents, environment, interactions and so on, is still lacking. This volume explores the state-of-the-art in the development of a real ABM ontology to address the epistemological issues related to this emerging paradigm for modeling complex systems.

Finance, Econometrics and System Dynamics presents an overview of the concepts and tools for analyzing complex systems in a wide range of fields. The text integrates complexity with deterministic equations and concepts from real world examples, and appeals to a broad audience.

"This set of books represents a detailed compendium of authoritative, research-based entries that define the contemporary state of knowledge on technology"--Provided by publisher.

Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.

Unconventional computing is the quest for groundbreaking new algorithms and computing architectures based on and inspired by the principles of information processing in physical, chemical and biological systems. The timely scientific contributions in this book include cutting-edge theoretical work on quantum and kinematic Turing machines, computational complexity of physical systems, molecular and chemical computation, processing incomplete information, physical hypercomputation, automata networks and swarms. They are nicely complemented by recent results on experimental implementations of logical and arithmetical circuits in a domino substrate, DNA computers, and self-assembly. The book supports interdisciplinary research in the field of future computing and contributes toward developing a common interface between computer science, biology, mathematics, chemistry, electronics engineering, and physics.

Complex Systems and Computation in Public Health Sciences is the first comprehensive book in population health science that meaningfully integrates complex systems theory, methodology, modeling, computational simulation, and real-world applications while incorporating current population health perspectives.

The spontaneous formation of well organized structures out of germs or even out of chaos is one of the most fascinating phenomena and most challenging problems scientists are confronted with. Such phenomena are an experience of our daily life when we observe the growth of plants and animals. Thinking of much larger time scales, scientists are led into the problems of evolution, and, ultimately, of the origin of living matter. When we try to explain or understand in some sense these extremely complex biological phenomena it is a natural question, whether pro cesses of self-organization may be found in much simpler systems of the un animated world. In recent years it has become more and more evident that there exist numerous examples in physical and chemical systems where well organized spatial, temporal, or spatio-temporal structures arise out of chaotic states. Furthermore, as in living of these systems can be maintained only by a flux of organisms, the functioning energy (and matter) through them. In contrast to man-made machines, which are to exhibit special structures and functionings, these structures develop spon devised It came as a surprise to many scientists that taneously-they are self-organizing. numerous such systems show striking similarities in their behavior when passing from the disordered to the ordered state. This strongly indicates that the function of such systems obeys the same basic principles. In our book we wish to explain ing such basic principles and underlying conceptions and to present the mathematical tools to cope with them.