The work carried out qualitative and quantitative study of the patterns of interaction of populations that form the basis of modern mathematical ecology. A qualitative analysis of the simplest model of the classical model of the “predator–prey” Volterra–Lotka by bringing it to a form that contains a controlled setting. The necessity of transition from Malthusian model to model with the logistic growth function. It is shown that in this system there is a stationary point. It builds a simple model taking into account the population density of the territory of the victims and predator’s mortality functions, depending on the size of the prey population. A model of the predator–multiple victims. The model is adapted on account of the interaction of predators with several kinds of victims, bearing in mind that victims also put pressure on each other. Built function that allows you to set a limit of “saturation” of the range of special, which was based on the equilibrium level of the populations of both victims and predators. A study of non–classical model of the “predator–prey” with trophic predator function, which depends on the ratio of the densities of populations of predators and prey. The expediency of using as an analytical research platform of simulation system AnyLogic, allowing use all known modeling concepts. A comprehensive study of the classical model of Volterra–Lotka. The phase portraits of the system taking into account the change system parameters and initial conditions. Parametric analysis of the influence coefficient model on populations. The results of the modeling and the analysis of models with logistic growth function of population size, model “predator–victim two” model taking into account the effect of the available space. The quantitative study of the non–classical model, taking into account the influence of the parameters of initial data and initial conditions on the phase portrait of the system.