The essence of dynamic economic behavior of competing economic entities, which simulated nonlocal problem for systems of differential equations with variable coefficients is revealed. Developed a dynamic mathematical model assuming that total production is determined by the following factors: the number of products each side, changing certain equipment, which leads to changes in output, the degree of distrust of competitors, and assuming that the rate of change in output proportional to these factors. A partial case of such a model is the model of the arms race. The economic interpretation of nonlocal conditions is that the production volumes at different times governed by predetermined condition. A mathematical model designed to study the dynamics of the economic process of adjusting production volumes at different times.