Publication Date



social dynamics, committed agents, bifurcation, center manifold


Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education


One of the most striking features of our time is the polarization, nationally and globally, in politics and religion. How can a society achieve anything, let alone justice, when there are fundamental disagreements about what problems a society needs to address, about priorities among those problems, and no consensus on what constitutes justice itself? This paper explores a model for building social consensus in an ideologically divided community. Our model has three states: two of these represent ideological extremes while the third state designates a moderate position that blends aspects of the two extremes. Each individual in the community is in one of these three states. A constant fraction of individuals are committed agents dedicated to the third, moderate state, while all other moderates and those from either extreme are uncommitted. The states of the uncommitted may change as they interact, according to prescribed rules, at each time step with their neighbors; the committed agents, however, cannot be moved from their moderate position, although they can influence neighbors. Our main objective is to investigate how the proportion of committed agents affects the large-scale dynamics of the population: in other words, we examine the special role played by those committed to embracing both sides of an ideological divide. A secondary but equally important goal is to gently introduce important dynamical systems concepts in a natural setting. Finally, we briefly outline a model with different interaction rules, a fourth state representing those who loathe the other three states, and agents who may be committed to any one of the four states.

BinaryConsensusMATLAB.zip (3 kB)
MATLAB code for the Binary Consensus model

BinaryPersusasionMATLAB.zip (2 kB)
MATLAB code for the Binary Persuasion model

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License



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