Handbook of Research Methods in Complexity Science
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Handbook of Research Methods in Complexity Science

Theory and Applications

Edited by Eve Mitleton-Kelly, Alexandros Paraskevas and Christopher Day

This comprehensive Handbook is aimed at both academic researchers and practitioners in the field of complexity science. The book’s 26 chapters, specially written by leading experts, provide in-depth coverage of research methods based on the sciences of complexity. The research methods presented are illustratively applied to practical cases and are readily accessible to researchers and decision makers alike.
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Chapter 15: Phase transitions and social contagion as enabling mechanisms for coordinated action in populations: a mathematical framework

Professor James K. Hazy and Professor Peter R. Wolenski


The chapter presents a general mathematical framework to study discontinuous change in human interaction dynamics. There are two complementary perspectives: macro and micro. Regarding the macro context, the chapter proposes that levels of ordered structure in complex human organizing can be represented by a category theoretic representation that reflects informational influence acting on individual agents from sources external to the population and those internal to the population. These independent influences interact to change the set of interaction rules that are enacted locally. Regarding micro context, the authors position contagion as the mechanism whereby a common organizing state is adopted across multiple agents. They show that as a general matter, the ordered structure that emerges within a population can be indexed as the number of active degrees of freedom embedded in local rules of interaction that are guiding groups of agents. Category theoretic mathematical approaches should be more used in social science research to suggest deductive hypotheses that can be tested empirically with definitive results.

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