INFORMATION TECHNOLOGY FOR CALCULATING MATHEMATICAL MODELS OF DYNAMICS OF TWO POPULATIONS

buckwheat flour have a higher protein content with the best amino acid content [4-5]. It is known that the combined consumption of zinc with proteins promotes its better absorption [6]. Thus, the introduction of new cake products of pumpkin seeds and buckwheat flour to replace traditional raw materials will increase zinc in combination with other biologically active components. Consumption of new flour confectionery products will have a positive effect on strengthening human immunity, which is especially important in today's complex environmental conditions.

. if periods of growth exponentially are interrupted by epidemics and natural disasters. In 1970, P.R. Ehrlich and A.H. Ehrlich in 1972, W.H. Meadows and others also examined exponential population growth and depletion of non-renewable natural resources [1,2].
Models that describe, with a certain degree of accuracy, individual events relating to the growth of the number of species could be created. Models can be not only from a descriptive, empirical view, but also general purpose (R.M. May "Stability and Complexity in Model Ecosystems", 1972) [3]. This distinction is especially important in relation to specific applications. In 1972, G. R. Conway and G. Murdie in "Population Models as a Basis for Pest Control" described models that can be used to select pest control products [4]. The range of these models is relatively narrow: from auxiliary models that describe, for example, sexual and territorial behaviour, to models designed to describe very small fragments of the biological system. Models of this type are intended to answer questions regarding a particular species, and not to study general environmental laws. In the terminology of C. S. Holling from "The Strategy of Bilding Models of Complex Ecological Systems" (1966) and "The Tactics of Predator" (1968), such models are called "tactical" [5,6]. The general strategic model creates a schema of the most important biological processes.
The purpose of the work is the implementation of the mathematical model of "predator-prey" in the form of a software application. The program should be able to monitor the dynamics of the population in the form of graphs of the number of predators and preys over time and a phase portrait of the system.
The host-parasite and predator-prey systems are examples of complex interactions when the development of an attacking species completely or partially depends on the number of individuals available to it used as a food source. The growth rate of the prey species depends on the number of individuals in a given population that are killed by a population of predators or parasites. The development of predator-prey models makes it possible to find out a number of important biological and mathematical properties of the system [7][8][9][10].
If we assume that the fertility of predators depends on the number of prey N t and the mortality of prey is proportional to the number of predators, then the rate of change in populations will be determined by equations: called the Lotka-Volterra equations. They suggest that in the absence of predators the prey population has an exponential growth (according to T. R. Maltus) [7] t n t N r dt dN  . (2) In equations (1) r n is the intrinsic rate of increase in the prey population, which decreases (for each given moment in time t) depending on the size of the predator population P t at the moment according to a linear law. Suppose that in the absence of a prey, predators die. Then their number decreases with speedr р . The latter is compensated by the multiplication factor с2 for a separate individual with a total number of prey N t [7,8].
Consider the relation which, after simplification, reduces to the following: Integrating, we get Equality (5) corresponds to a set of closed curves connecting P t and N t (Fig.  1a), and the constant is determined only by the initial values of the numbers N0 and  To develop an information technology for calculating the dynamics model of two populations, the Delphi programming language was used [11,12]. To calculate the model and obtain graphs of the number of populations and phase trajectories, it is necessary to enter the number of preys, predators and the number of calculation steps (Fig. 2). After that, you need to click the "calculate" button and get the result.
The program calculates step-by-step the population size (left) and shows the dependence of the number of predators and preys on time (right), as well as a phase portrait -a sequential display of points corresponding to the state of the system in phase space. For the predator-prey model, the phase space can have two dimensions -the number of predators and the number of preys. Conclusions. The work describes the predator-prey system. Based on the mathematical model, a software application for calculating biological populations of the predator-prey system has been developed using Delphi programming language. The program has the ability to display the dynamics of the population in the form of graphs of the number of predators and preys in time and phase portrait of the system. In view of growing competition in the freight market in recent years, shipowners are forced to take active measures aimed at improving the efficiency of their own fleet. In this connection, there is a need for a deeper analysis of the trends in the structure of freight flows and a more accurate choice of the fleet development strategy. Of great importance is timely replacement of vessels and replenishment of the fleet with such vessels, which would allow to work as efficiently and flexibly as possible in conditions of tough competition and uneven structure of cargo traffic.

References:
The basic principles of modern oversized project cargo transportation, stowage and securing technologies are discussed in articles [1,2]. The issue of optimum terms of purchase and sale of vessels and other equipment was considered in [3][4][5][6][7], taking into account the factor of uncertainty. The issue of optimal time to enter the shipping market was studied in [8][9][10]. One of the key methods aimed at shipping efficiency improvement is concerned with lowering fuel consumption by reducing ship speed. Papers [11,12] examine the dependence of vessel's operation efficiency indicators on ship speed. The profitability of ship speed reduction and fuel consumption of seagoing bulk carriers was examined in [3,[8][9][10][11][12].