## 1 Introduction
The differential equations of a time domain present in the Forrester diagram are transformed into a frequency domain based on the Laplace transform to facilitate obtaining the output equation, and explain the behavior of state variables in the simulation model. The conventional control engineering technique is used to present and reduce the SD model in a block diagram as a mechanism for determining the structure of the system. The direct path equation and the feedback equation are determined to obtain mathematical models that explain the particular trajectory of the behavior of each state variable through a transfer function in response to the different inputs of the system, in relation to a ratio, which relates the response of a system to an input or excitation signal. The output signal and the input signal of the dynamic system are represented by algebraic polynomials in the frequency domain. The roots of the denominator polynomial represent the poles of the transfer function to define the stability of the external dynamics of the system through their interpretation in a diagram of roots or poles and zeros. The roots of the numerator polynomial represent the zeros of the transfer function to weight the system's response to the input or excitation signal. Having the construction and understanding of the SD model, currently the validation of the models is performed by the means of a sensitivity analysis, which consists of a systematic study of how the conclusions of a model are affected by possible variations in parameter values and the functional relationships it includes. The simplest way to perform the analysis is to modify the numerical values of each of its parameters. For this purpose, the value of the parameter whose sensitivity is to be studied is increased by a certain percentage, and the extent to which this variation affects the conclusions of the model (the trajectories it generates) is analyzed. Manual sensitivity analysis requires changing the value of a constant (or several constants at once) and simulating, changing the value of the constant again and simulating again, and repeating this action many times to achieve a spectrum of output values [6]. Today, there are thousands of important applications in the environmental, business, social and scientific sector, developing SD simulation models with a great impact at industrial and academic level, such as [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. The developed models of SD presented in the field of energy, medicine, agriculture, population development, industry 4.0 and sustainability are of great value. In the validation of all the models cited, they use the technique of sensitivity analysis to validate the models, generating multiple scenes and changes in critical variables subjectively, and analyzing changes in their behavior. Since there are multiple variables and interactions in the systems dynamics models, and only the interpretation of the results obtained, it is difficult and complex to identify which parameters should be chosen to perform the sensitivity analysis. It is evident that an area of opportunity exists to define a mathematical model to identify parameters that affect behavior in a simple, analytical and objective way, rather than the current subjective choice. The present research proposes an analytical alternative of analysis for SD models, which is able to explain the behaviors of state variables, obtaining a mathematical model that explains its external dynamics and controls the particular trajectory of each behavior, instead of just observing the response without understanding whether or not there is any relation to the output in relation to the input of the model under study. In addition, by determining the transfer function, it is possible to analyze and monitor the response to multiple changes in the inputs to the system, the fundamental reason and motivation of this research project.