Abstract
The features of computer simulation of the biological system «Predator-prey» discussed. As predators feed on prey, prey starts to decrease and predators start to increase. However, this may not last long. After a while, predators do not have enough food, and their population stops growing and even decreases. As a result, the victims begin to multiply and their number increases. Then these processes are repeated and begin to determine the periodicity. Models describing the Predator-Prey biological system are quite common, the most common being the Lotka-Volterra model, the Lotka-Volterra model with a logistic correction, and the Holling-Tanner model. The paper presents computer simulation and description of these phenomena using the modern system of computer mathematics Mathcad. Mathcad is ideal for modeling and visualizing various phenomena. For the first time, a comparative analysis of the results of the three above models was carried out. The analysis showed the following: The Lotka-Volterra model is quite universal. It can describe not only changes in predator and prey populations, but also the behavior of competing firms, population growth, the size of warring armies, changes in the environmental situation, the development of science, etc. Fluctuations in predator and prey populations are actually not always observed. Often we observe a stable number of both, although the process of eating prey by predators is ongoing. Such a case requires the introduction of some logistic correction, which is taken into account in the Lotka-Volterra model with a logistic correction. The nonlinearity of the Holling-Tanner model is quite strong, which can be seen from the appearance of the phase portrait, the turns of which differ markedly from ellipses. The main property of this model is that, ultimately, the oscillations are set by the limit cycle of the phase portrait, which can be stable. It determines the amplitude of the oscillations, which are set in the stationary mode of the system. In this case, oscillations can both decay in time and increase in time, approaching stationary oscillations