Introduction to the Theory of Complex Systems

ISBN : 9780198821939

Stefan Thurner; Peter Klimek; Rudolf Hanel
480 ページ
171 x 246 mm
  • A self-contained introduction, providing comprehensive coverage of the field
  • Tackles the vast terrain of complex systems, by mapping them onto a simple framework

This book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it ecosystems, societies, traffic, financial markets, opinion formation and spreading, or the internet and social media. Complex systems are systems composed of many elements that interact strongly with each other, which makes them extremely rich dynamical systems showing a huge range of phenomena. Properties of complex systems that are of particular importance are their efficiency, robustness, resilience, and proneness to collapse.
The quantitative tools and concepts needed to understand the co-evolutionary nature of networked systems and their properties are challenging. The book gives a self-contained introduction to these concepts, so that the reader will be equipped with a toolset that allows them to engage in the science of complex systems. Topics covered include random processes of path-dependent processes, co-evolutionary dynamics, dynamics of networks, the theory of scaling, and approaches from statistical mechanics and information theory. The book extends beyond the early classical literature in the field of complex systems and summarizes the methodological progress made over the past 20 years in a clear, structured, and comprehensive way.


1: Introduction to complex systems
2: Probability and random processes
3: Scaling
4: Networks
5: Evolutionary processes
6: Statistical mechanics & information theory for complex systems
7: The future of the science of complex systems?
8: Special functions and approximations


Stefan Thurner, Full Professor of Science of Complex Systems, Medical University of Vienna, Austria, Rudolf Hanel, Associate Professor, Medical University of Vienna, Austria, and Peter Klimek, Associate Professor, Medical University of Vienna, Austria
Stefan Thurner is full professor for Science of Complex Systems at the Medical University of Vienna, where he chairs the Section for Science of Complex Systems. He is external professor at the Santa Fe Institute, senior researcher at IIASA, and president of the Complexity Science Hub Vienna. He obtained a PhD in theoretical physics from the Technical University of Vienna and a PhD in economics from the University of Vienna. He held postdoctoral positions at Humboldt Universität zu Berlin and Boston University before joining the faculty of the University of Vienna and later Medical University. Stefan started his career with contributions to theoretical particle physics and gradually shifted his research focus to the understanding of complex systems. He is the author of more than 200 scientific articles.
Peter Klimek is Associate Professor at the Section for Science of Complex Systems at the Medical University of Vienna and faculty member of the Complexity Science Hub Vienna. His research interests include network medicine, complexity economics, modelling of collective socio-economic phenomena, electoral fraud detection, as well as novel methods to measure systemic risk.
Rudolf Hanel is Associate Professor at the Section for Science of Complex Systems at the Medical University of Vienna and faculty member of the Complexity Science Hub Vienna. His research interests range from applications in medical physics to theoretical work on the behaviour of driven regulatory systems with a focus on mathematical issues.

"This book will surely become a standard text for anyone who wants to seriously understand complexity no matter what their background or stage of career. It is written from a physicists perspective, stressing mechanism, underlying principles and mathematical rigour, yet is eminently readable and pedagogical." - Geoffrey West, Santa Fe Institute

"Complexity until now has been lacking a strong theoretical underpinning. Now it has one. This book is a tour de force. Excellent!" - W. Brian Arthur, Santa Fe Institute