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Modeling Trade Wars: Applying Systems of Ordinary Differential Equations
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Morris, Jason
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2022-12-09
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Systems of differential equations have been used to model a variety of situations
including population dynamics, reactions between several chemicals, and even the outcome of
warfare between two nations. These types of systems are well equipped to model both simple
and relatively complex situations involving several interacting parties; however, they seem to
have never been used to model the interactions between nations engaged in a trade war. This text
was primarily developed to showcase the ability of such systems to broadly model the key
features of such a trade conflict. We begin by summarizing the main inputs and outputs of
several historical trade wars and proceed forward by developing two models utilizing systems of
differential equations that incorporate these inputs and outputs into their terms. Following this,
we analyze both systems by finding specific solutions to each, by developing a general formula
for each system’s equilibria, and by confirming the stability of these equilibria. After the model’s
development and analysis, we apply these systems in the controlled environment of a
hypothetical trade war. Finally, we conclude with a brief list of limitations that discuss several
factors that hinder the accuracy of the proposed models.
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