ABSTRACT
This chapter illuminates essential dynamics of complex, and crucially important, social systems. It shows that mathematical biology offers a powerful, and hitherto underexploited, perspective on both interstate and intrastate social dynamics. The chapter explores the unifying power of mathematics, and specifically, of nonlinear dynamical systems theory; formal analogies between seemingly disparate social and biological phenomena are highlighted. It stimulates reconstruction in mathematical social science, relaxing—in some cases abandoning—the predominant assumption of perfectly informed utility maximization, and exploring social dynamics from such perspectives as epidemiology and ecosystem science. The chapter discusses the combination of arms race and epidemiology perspectives in building a simple model of the spread of drug addiction in an idealized community, revealing basic, and perhaps counterintuitive, relationships between legalization, prices, and crime. It assumes familiarity with vector calculus, linear differential equations, eigenvalue-eigenvector methods, phase plane analysis, and certain elements of complex variables, real analysis, and partial differential equations.
