This is a mathematical study of the diffusion of collective action. It develops mathematical models of the diffusion of collective action in cycles or waves of protest, with a particular emphasis on the diffusion of collective violence and disruptive collective protest and the ways these are affected by cycles of non-disruptive protest, the formation and institutionalization of movement organizations, and the social control efforts of regimes. Recent advances in event-history models of diffusion are used as the basis for further development of diffusion models which capture temporal and spatial heterogeneity and which adequately capture the ebbing phase of a cycle as well as its rise. Multiple-equation models are developed for the interplay among different forms of action and between regimes and dissidents. Computer simulation technologies are used to investigate the full response surface of all models, showing how the incidence of various forms of actions varies with the full range of possible combinations of independent variables. Models are developed to represent important phenomena for which there is a body of solid empirical data, including several waves of collective violence, and the protest cycles of the US Civil Rights Movement in 1950-1990 and the "new social movements" of Europe in 1975-1990. These models are parameterized to be consistent with known data, but include variables and relationships which remain speculative and unobserved in published accounts. Alternate explanatory mechanisms are rigorously explored and tested for goodness of fit against available data. %%% This project is a contribution to abstract, mathematical sociology. It will develop rigorous formal theory which is capable of identifying general patterns and mechanisms which transcend specific cases but which can be meaningfully tested against empirical data. Thus it will strengthen the fundamental intellectual basis upon which more applied or policy-oriented studies must rest.
