Differential Systems: Applications

Abstract

There are many processes in the world that can be modeled by systems of differential equations. In biology, modeling competing species requires coupled systems of nonlinear equations. Chemical mixing problems involving a single solute dissolved in solutions throughout several interconnected containers whose contents are being intermixed, require one differential equation for the amount of solute in each container. In physics, mechanical systems involving multiple springs and multiple masses in various configurations introduce linear (and sometimes nonlinear) systems of differential equations. In electrical engineering, passive L-R-C circuits having multiple loops and hence multiple currents require a system of linear differential equations, one equation for the current in each loop. In fact, passive L-R-C circuits are modeled by a hybrid set of equations consisting of several differential equations and several algebraic equations all to be satisfied simultaneously. In international relations, a linear system of equations proposed by Richardson¹ effectively models the forces that govern the armament and disarmament of nations that do not trust one another.