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Mathematical sociology

In collaboration with R. E. Niemeyer and under the auspices of the AMIS lab (Applications of Mathematics and Integrated Science), we examine the effect of particular parameter changes in a system of ordinary differential equations modeling the interaction between people of a nation-state, the amount of internal strife and the amount of resources within the system.

Peter Turchin et al, construct a system of ordinary differential equations that accurately models the rise and fall of particular empires. However, they do not fully examine the robustness of their model, nor do they fully justify the simplification of a 3D system to a 2D system. While their work is empirically sound, we argue that one does not need to reduce the complexity of the system by collapsing the state resources variable S and the internal strife variable W into a new variable I, called the instability index. If one maintains the conjecture that all three variables are important in describing the rise and fall of an empire, then other dynamical systems may provide better explanatory power and insight into how to predict the effect of diminishing resources in a city-state and an increase in internal strife.