In the 1930s L. F. Richardson proposed that an arms race between two countries could be
Chapter 11, Problem 22(choose chapter or problem)
In the 1930s L. F. Richardson proposed that an arms race between two countries could be modeled by a system of differential equations. One arms race that can be reasonably well described by differential equations is the USSoviet Union arms race between 1945 and 1960. If $x represents the annual Soviet expenditures on armaments (in billions of dollars) and $y represents the corresponding US expenditures, it has been suggested33 that x and y obey the following differential equations: dx dt = 0.45x + 10.5 dy dt = 8.2x 0.8y 142. (a) Find the nullclines and equilibrium points for these differential equations. Which direction do the trajectories go in each region? (b) Sketch some typical trajectories in the phase plane. (c) What do these differential equations predict will be the long-term outcome of the US-Soviet arms race?
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