Applying Dynamical Systems to Sociology
Christopher Strohmeier
Continuous dynamical systems is an immense field of mathematics whose origins may be traced to the work of Newton. It seeks to describe physical phenomena through the means of ordinary differential equations, i.e. equations which relate the values of a function to rates of change of said function. The attached article introduces the elementary theory of dynamical systems along with the notion of chaos/instability.
The beautiful thing about dynamical systems is that they may be used to model essentially any phenomena which involves change. For example, the technique of drawing the phase diagram (top of page 29) is extremely useful for understanding network effects, which were discussed in chapter 17 of the course textbook. In particular, one may use an analogous diagram to detect equilibria of markets with network effects and to determine their stability. For example, if the arrows drawn in the diagram point inward to a given equilibrium point, then said equilibrium point is unstable. If any one adjacent arrow points away from the point, then it cannot be stable.
Link:
http://faculty.washington.edu/joelzy/402_notes_bernard.pdf