Introduction: The pigeons (Columba livia) are a cultural part of the historical centers of the great cities of the world; however, they are an invasive species that can become a threat to the public health of visitors to the Plaza de Bolívar in Bogotá, which is why it is necessary to control the net increase of these birds, without seeking extinction. Objective: In this work a mathematical model of the population growth of pigeons was constructed, under a series of control pulses through time, to observe the behavior of controlled development of these birds. Materials and Methods: As a main tool we used the modeling methodology known as System Dynamics, which allows us to obtain a system of differential equations from a systemic representation of a problem. Results: The results indicate that the simulation of this type of control allows the population of pigeons to remain within an acceptable range for space. Conclusions: This work is considered a great contribution in the simulation and evaluation of scenarios for the population control of pigeons, through the evaluation with Systems Dynamics and can be reproduced for other problem species.