Abstract:

Modelling and simulation are essential tools for understanding the world around us and the way it works. Mathematicians found a way to describe the real-world phenomena into differential equations. Furthermore, it gives us a tool for finding solutions for major problems like overpopulation and overproduction. In theory, one can make a model for a sample country’s population and simulate its behavior. By doing so it is possible to predict how many people will live in that area in 5 years. For making complex models like the mentioned, first we should understand the essential ones.

The aim of this paper is to develop an application and test it with the students. The user can parameterize some single-population (exponential, logistic, etc.) and multi-population (predation, competition etc.) models in discrete and continuous cases. Another goal is that the values calculated in each model should be easily interpreted. Because of this the program places significant emphasis on visualization as well. From the numerical results the user may see the population size in a specific time while the visualization displays the behavior of the model. If necessary, it is possible the analyze the model in detail. One of the notable analytical aspects is the estimation of population number changes over time. If solution exists for the concrete case, it is called an equilibrium solution. The designed program can calculate the mentioned solutions and offers multiple options for visualization.

The models are mainly created through experience, which is why the hands-on learning method can be used in the educational process. Students are given the opportunity to modify the parameters of each model and draw their own conclusions. Our goal is to indirectly help the students to form conjectures while experimenting with the software. The accuracy of the calculated prediction depends on the input preferences. Carefully built models may describe real world phenomena with high precision.

Keywords:

Hands-on learning, modelling, simulation, visualization, population, application.