Nonlinear Dynamics and Chaos in Arms Race Models

Abstract

We discuss several nonlinear generalizations of the classical arms race models of L.F. Richardson. We consider models with discrete time evolutions and economic constraints. For two nation models one can find chaotic solutions in perfectly symmetric cases. For three nation models and the possibility of alliance formation, we can find large stable regions for simple approaches to arms-control fixed points separated by control surfaces at which critical changes of alliances occur. In a more specific arms race model which involves three different strategic weapons systems we discuss different types of stable and unstable solutions of scenarios related to the introduction of strategic defense (SDI) systems. Armsraces between two nations in which decisions are based on the power distribution within each of the nations are simulated in a discrete generalization of Kadyrov models of two coupled cusp control surfaces.KeywordsChaotic AttractorExternal ThreatStable Fixed PointChaotic SolutionReentry VehicleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.