How does a mathematical model describe interactions within a system?

In systems engineering, a mathematical model serves as a quantitative tool to describe the interactions within a system. While qualitative methods like flowcharts are useful for initial studies, a mathematical model provides a more effective, rigorous approach by representing these interactions through a set of equations, tables, or curves.1

These models do not need to be exact to be useful; they often employ piecewise linear approximations to represent complex, nonlinear situations as a series of manageable segments. Once constructed, engineers apply various mathematical techniques—often involving probabilistic or statistical calculations—to analyze the system's actual operation.1

This quantitative description is essential for performing trade-off studies. By modeling how subsystems interact, engineers can determine how limited performance in one area might be offset by superior performance elsewhere. This allows for the optimization of the system, helping to identify the most economical way to achieve a goal or to evaluate whether a proposed performance target is reasonable.1