Introduction to the Theory of Complex Systems

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.

這本書是對複雜適應系統的量化方法的全面介紹。實際上，地球上的幾乎所有領域都不斷面臨著複雜系統，無論是生態系統、社會、交通、金融市場、意見形成和傳播，還是互聯網和社交媒體。複雜系統是由許多元素組成並彼此強烈相互作用的系統，這使得它們成為極其豐富的動態系統，展示出廣泛的現象。複雜系統的特性對於其效率、穩健性、彈性和崩潰易感性具有特殊重要性。

理解網絡系統的共同演化性質及其特性所需的量化工具和概念具有挑戰性。本書提供了對這些概念的自包含介紹，使讀者能夠掌握一套工具，從而參與複雜系統科學。涵蓋的主題包括隨機過程、路徑相依過程、共同演化動力學、網絡動力學、縮放理論以及統計力學和信息理論的方法。本書超越了複雜系統領域早期的經典文獻，以清晰、結構化和全面的方式總結了過去20年在方法論上取得的進展。