Adding one and one makes two, usually. But sometimes things add up to more than the sum of their parts. This observation, now frequently expressed in the maxim "more is different", is one of the characteristic features of complex systems and, in particular, complex networks. Along with their ubiquity in real world systems, the ability of networks to exhibit emergent dynamics, once they reach a certain size, has rendered them highly attractive targets for research. The resulting network hype has made the word "network" one of the most in uential buzzwords seen in almost every corner of science, from physics and biology to economy and social sciences. The theme of "more is different" appears in a different way in the present v- ume, from the viewpoint of what we call "adaptive networks." Adaptive networks uniquely combine dynamics on a network with dynamical adaptive changes of the underlying network topology, and thus they link classes of mechanisms that were previously studied in isolation. Here adding one and one certainly does not make two, but gives rise to a number of new phenomena, including highly robust se- organization of topology and dynamics and other remarkably rich dynamical beh- iors.

In the last years, adaptive networks have been discovered simultaneously in different fields as a universal framework for the study of self-organization phenomena. Understanding the mechanisms behind these phenomena is hoped to bring forward not only empirical disciplines such as biology, sociology, ecology, and economy, but also engineering disciplines seeking to employ controlled emergence in future technologies. This volume presents new analytical approaches, which combine tools from dynamical systems theory and statistical physics with tools from graph theory to address the principles behind adaptive self-organization. It is the first class of approaches that is applicable to continuous networks. The volume discusses the mechanisms behind three emergent phenomena that are prominently discussed in the context of biological and social sciences: synchronization, spontaneous diversification, and self-organized criticality. Self-organization in continuous adaptive networks contains extended research papers. It can serve as both, a review of recent results on adaptive self-organization as well as a tutorial of new analytical methods Self-organization in continuous adaptive networks is ideal for academic staff and master/research students in complexity and network sciences, in engineering, physics and maths. Contents: Introduction; 1. Concepts and Tools; 2. Topological stability criteria for synchronized states; 3. Patterns of cooperation; 4. Self-organized criticality; 5. Conclusions and future research; Bibliography; Keyword Index; List of abbreviations.

Adding one and one makes two, usually. But sometimes things add up to more than the sum of their parts. This observation, now frequently expressed in the maxim "more is different", is one of the characteristic features of complex systems and, in particular, complex networks. Along with their ubiquity in real world systems, the ability of networks to exhibit emergent dynamics, once they reach a certain size, has rendered them highly attractive targets for research. The resulting network hype has made the word "network" one of the most in uential buzzwords seen in almost every corner of science, from physics and biology to economy and social sciences. The theme of "more is different" appears in a different way in the present v- ume, from the viewpoint of what we call "adaptive networks." Adaptive networks uniquely combine dynamics on a network with dynamical adaptive changes of the underlying network topology, and thus they link classes of mechanisms that were previously studied in isolation. Here adding one and one certainly does not make two, but gives rise to a number of new phenomena, including highly robust se- organization of topology and dynamics and other remarkably rich dynamical beh- iors.