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Using An Arms Race Model To Illustrate Key Concepts & Techniques in a First Differential Eq Course

Presented by: Michael Olinick, Middlebury College, Middlebury VT USA https://qubeshub.org/community/groups... Abstract: The Richardson Arms Race Model describes the dynamics of arms expenditures of two nations, each of which is driven to increase its spending by the spending level of its rival, but faces internal resistance as its own expenditures grow and experiences external drivers of good or ill will. The classic formulation of the model is a linked system of two first order linear differential equations. Phase plane analysis of the model early in a differential equations course reveals the possibilities of sinks, sources, and saddle points. Students can find exact solutions using eigenvalues and eigenvectors in the middle of the term. They can explore more realistic models by replacing the constant parameters with their own choices of continuous functions and apply numerical solution methods to simulate the behavior later in the semester. In an advanced DE course, delay differential equations can replace the ODEs as neither nation may be able to change its arms budget instantaneously in response to its opponent.