Thinking in Complexity

Thinking in Complexity
Author: Klaus Mainzer
Publisher: Springer Science & Business Media
Total Pages: 357
Release: 2013-03-09
Genre: Science
ISBN: 3662033054

Since the first edition sold out in less than a year, we now present the revised second edition of Mainzer's popular book. The theory of nonlinear complex systems has become a successful problem-solving approach in the natural sciences from laser physics, quantum chaos, and meteorology to computer simulations of cell growth in biology. It is now recognized that many of our social, ecological, and political problems are also of a global, complex, and nonlinear nature. And one of the most exciting contemporary topics is the idea that even the human mind is governed largely by the nonlinear dynamics of complex systems. In this wide-ranging but concise treatment, Prof. Mainzer discusses, in a nontechnical language, the common framework behind these endeavors. Emphasis is given to the evolution of new structures in natural and cultural systems and we see clearly how the new integrative approach can give insights not available from traditional reductionistic methods.

Models of Science Dynamics

Models of Science Dynamics
Author: Andrea Scharnhorst
Publisher: Springer Science & Business Media
Total Pages: 292
Release: 2012-01-24
Genre: Social Science
ISBN: 3642230687

Models of Science Dynamics aims to capture the structure and evolution of science, the emerging arena in which scholars, science and the communication of science become themselves the basic objects of research. In order to capture the essence of phenomena as diverse as the structure of co-authorship networks or the evolution of citation diffusion patterns, such models can be represented by conceptual models based on historical and ethnographic observations, mathematical descriptions of measurable phenomena, or computational algorithms. Despite its evident importance, the mathematical modeling of science still lacks a unifying framework and a comprehensive study of the topic. This volume fills this gap, reviewing and describing major threads in the mathematical modeling of science dynamics for a wider academic and professional audience. The model classes presented cover stochastic and statistical models, system-dynamics approaches, agent-based simulations, population-dynamics models, and complex-network models. The book comprises an introduction and a foundational chapter that defines and operationalizes terminology used in the study of science, as well as a review chapter that discusses the history of mathematical approaches to modeling science from an algorithmic-historiography perspective. It concludes with a survey of remaining challenges for future science models and their relevance for science and science policy.

Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems
Author: Robert A. Meyers
Publisher: Springer Science & Business Media
Total Pages: 1885
Release: 2011-10-05
Genre: Mathematics
ISBN: 1461418054

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.

Historical Dynamics

Historical Dynamics
Author: Peter Turchin
Publisher: Princeton University Press
Total Pages: 260
Release: 2018-05-08
Genre: History
ISBN: 1400889316

Many historical processes are dynamic. Populations grow and decline. Empires expand and collapse. Religions spread and wither. Natural scientists have made great strides in understanding dynamical processes in the physical and biological worlds using a synthetic approach that combines mathematical modeling with statistical analyses. Taking up the problem of territorial dynamics--why some polities at certain times expand and at other times contract--this book shows that a similar research program can advance our understanding of dynamical processes in history. Peter Turchin develops hypotheses from a wide range of social, political, economic, and demographic factors: geopolitics, factors affecting collective solidarity, dynamics of ethnic assimilation/religious conversion, and the interaction between population dynamics and sociopolitical stability. He then translates these into a spectrum of mathematical models, investigates the dynamics predicted by the models, and contrasts model predictions with empirical patterns. Turchin's highly instructive empirical tests demonstrate that certain models predict empirical patterns with a very high degree of accuracy. For instance, one model accounts for the recurrent waves of state breakdown in medieval and early modern Europe. And historical data confirm that ethno-nationalist solidarity produces an aggressively expansive state under certain conditions (such as in locations where imperial frontiers coincide with religious divides). The strength of Turchin's results suggests that the synthetic approach he advocates can significantly improve our understanding of historical dynamics.

Nonlinear Dynamics, Chaos, and Complexity

Nonlinear Dynamics, Chaos, and Complexity
Author: Dimitri Volchenkov
Publisher: Springer Nature
Total Pages: 198
Release: 2020-12-14
Genre: Mathematics
ISBN: 9811590346

This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).

Systems Thinking, System Dynamics

Systems Thinking, System Dynamics
Author: Kambiz E. Maani
Publisher:
Total Pages: 278
Release: 2007
Genre: Management
ISBN: 9781877371035

Systems Thinking, System Dynamics offers readers a comprehensive introduction to the growing field of systems thinking and dynamic modelling and its applications. The book provides a self-contained and unique blend of qualitative and quantitative tools, step-by-step methodology, numerous examples and mini-cases, as well as extensive real-life case studies. The content mix and presentation style make the otherwise technical tools of systems thinking and system dynamics accessible to a wide range of people. This book is intended as a text for students in diverse disciplines including business and management, as well as the social, environmental, health and applied sciences. It also has particular relevance for professionals from all backgrounds interested in understanding the dynamic behaviour of complex systems, change management, complex decision making, group problem solving and organisational learning. Systems thinking and system dynamics provide a scientific paradigm, a set of tools and computer technology which can help explain the forces and dynamics that underlie change and complexity in business, political, social, economic and environmental systems. Using systems thinking and system dynamics makes it possible to: examine and foresee the consequences of policy and strategic decisions implement fundamental solutions to chronic problems avoid mistakenly interpreting symptoms as causes test assumptions, hypotheses and scenarios boost staff morale and improve productivity improve the stability and performance of supply chains find long-term sustainable solutions and avoid ‘fire-fighting’ behaviour.

Complexity, Management and the Dynamics of Change

Complexity, Management and the Dynamics of Change
Author: Elizabeth McMillan
Publisher: Routledge
Total Pages: 256
Release: 2008-08-28
Genre: Business & Economics
ISBN: 1134115121

Introducing the principles of complexity science, this innovative text illustrates how different kinds of organizational can become more effective, democratic and sustainable by using these powerful ideas.

Systems and Models

Systems and Models
Author: Hartmut Bossel
Publisher: BoD – Books on Demand
Total Pages: 374
Release: 2007
Genre: Science
ISBN: 3833481218

A multitude of complex systems and actors pursuing their own agenda shape the dynamics of our world. Better understanding of their actions and interactions is crucial, and can be achieved by a profound knowledge of systems and their properties, and their representation in models allowing simulation of probable behavior. Drawing on his extensive research and teaching experience in modeling and simulation of a wide range of systems - from engineering to social systems and ecosystems - the author presents the fundamental concepts and approaches for understanding and modeling the complex systems shaping the dynamics of our world. The book applies state space analysis and system dynamics to deal with the dynamic processes of "causal systems," discusses information processing approaches for modeling decision processes of "actors" and "agents," and uses aspects of the coevolutionary development of systems in their environment to deal with normative orientation, ethics, and evaluation of policies and long-term development. The concepts are applied in particular to the issue of sustainable development of human society in an evolving world. The book is complemented by a survey of system topics and of models from many fields, and by an extensive bibliography on the many systems-related subjects covered. Hartmut Bossel is Professor Emeritus of environmental systems analysis. He taught for many years at the University of California in Santa Barbara and the University of Kassel, Germany, where he was director of the Center for Environmental Systems Research until his retirement. He holds an engineering degree from the Technical University of Darmstadt, and a Ph.D. degree from the University of California at Berkeley. With a background in engineering, systems science, and mathematical modeling, he has led many research projects and future studies in different countries, developing computer simulation models and decision support systems in the areas of energy supply policy, global dynamics, orientation of behavior, agricultural policy, and forest dynamics and management. He has written numerous books on modeling and simulation of dynamic systems, social change and future paths, and has published widely in the scientific literature in several fields. Bossel is author of a System Zoo containing over one hundred simulation models of diverse systems.

Regularity and Complexity in Dynamical Systems

Regularity and Complexity in Dynamical Systems
Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
Total Pages: 503
Release: 2011-12-21
Genre: Technology & Engineering
ISBN: 1461415241

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.