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.
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 Universitat 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.
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