Introduction to the Theory of Complex Systems

Abstract

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, epidemic spreading, or the internet and social media. Complex systems are systems composed of many elements that interact 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 intention of the book is to give a self-contained introduction to these concepts so that the reader will be equipped with a conceptual and mathematical toolset that allows her to engage in the science of complex systems. Topics covered include random processes of path-dependent processes, co-evolutionary dynamics, the statistics of driven nonequilibrium systems, dynamics of networks, the theory of scaling, and approaches from statistical mechanics and information theory. The book extends well beyond the early classical literature in the field of complex systems and summarizes the methodological progress over the past twenty years in a clear, structured, and comprehensive way. The book is intended for natural scientists and graduate students.

Identifying general trends and patterns in complex systems research: An overview of theoretical and practical implications

“…In the vast body of literature that deals with introducing complexity theory, a few general trends are recognizable as summarized here below: Different fields of study inform different approaches and fundamental understandings of systems and complexity. There seems to be two very distinct approaches, namely, (a) “computational complexity” where the scientific foundations and relevance of complexity are derived from the capacity to quantify and simulate the behaviour, connections, structures, and phases of complex systems by means of mathematical equations, algorithms, and computational models (Thurner, Hanel, & Klimek, ) and (b) by extending the vocabulary of computational complexity to be translated into a qualitative engagement with the features of complexity, the approach called “critical complexity” (Audouin et al, ; Cilliers, ) can be identified that emerges from the philosophical and practical engagement with complex systems. This approach is not directed towards observing and analysing complexity but explores what it means to participate in and creatively coconstruct the phenomenological experiences of everyday instances and encounters of a messy, complex reality (Boulton et al, ). Theories of complexity are all concerned with the study of systemic phenomena in states of nonequilibrium that display instances of nonlinearity, self‐organization, emergence, and behave in a manner in which time and energy expenditure is irreversible (Arthur, ; Gell‐Mann, ; Prigogine, ).…”

Becoming Cognitive Science

“…By striving to create a general enough conception of minds to capture their diverse manifestations, cognitive science belongs to the relatively uncommon class of “integrative sciences.” This class also includes artificial life—creating software, robotic, and synthetic biological life forms to understand the essential nature of life abstracted beyond its DNA‐based forms (Agmon, Gates, Churavy, & Beer, ; Bedau, ; Horowitz & England, ). A third exemplar is complex systems, the general study of systems made up of parts that interact to create emergent, global patterns such as positive and negative feedback loops, oscillations, and recursive branching structures (Mitchell, ; Page & Miller, ; Thurner, Klimek, & Hanel, ). Interestingly, adaptation is a theme for all three of these integrative sciences, and some approaches subsume all three (Maturana & Varela, 1973/1980).…”

Physicist’s approach to public transportation networks: between data processing and statistical physics

“…For these reasons it comes as no surprise that over the last few decades physics (or at least physicists) has spread into a much wider field of analyzing problems which traditionally might have been thought to be the subject of other sciences. Here, physics seeks to better understand how simple rules lead to the diverse and cooperative behavior found in complex systems [41,72]. Such complex systems can be found in biology, sociology and in other disciplines where interactions between agents play important roles.…”