Статьи

The analysis of trajectory dynamics and the solution of optimization problems using computer methods are relevant areas of research in dynamic population-migration models. In this paper, four-dimensional dynamic models describing the processes of competition and migration in ecosystems are studied. Firstly, we consider a modification of the “two competitors—two migration areas” model, which takes into account uniform intraspecific and interspecific competition in two populations as well as non-uniform bidirectional migration in both populations. Secondly, we consider a modification of the “two competitors—two migration areas” model, in which intraspecific competition is uniform and interspecific competition and bidirectional migration are non-uniform. For these two types of models, the study is carried out taking into account the variability of parameters. The problems of searching for model parameters based on the implementation of two optimality criteria are solved. The first criterion of optimality is associated with the fulfillment of such a condition for the coexistence of populations, which in mathematical form is the integral maximization of the functions product characterizing the populations densities. The second criterion of optimality involves checking the assumption of the such a four-dimensional positive vector existence, which will be a state of equilibrium. The algorithms developed on the basis of the first and second optimality criteria using the differential evolution method result in optimal sets of parameters for the studied population-migration models. The obtained sets of parameters are used to find positive equilibrium states and analyze trajectory dynamics. Using the method of constructing self-consistent one-step models and an automated stochastization procedure, the transition to the stochastic case is performed. The structural description and the possibility of analyzing two types of population-migration stochastic models are provided by obtaining Fokker–Planck equations and Langevin equations with corresponding coefficients. Algorithms for generating trajectories of the Wiener process, multipoint distributions and modifications of the Runge–Kutta method are used. A series of computational experiments is carried out using a specialized software package whose capabilities allow for the construction and analysis of dynamic models of high dimension, taking into account the evaluation of the stochastics influence. The trajectory dynamics of two types of population-migration models are investigated, and a comparative analysis of the results is carried out both in the deterministic and stochastic cases. The results can be used in the modeling and optimization of dynamic models in natural science.

In recent years, artificial intelligence methods have been developed in various fields, particularly in education. The development of computer systems for student learning is an important task and can significantly improve student learning. The development and implementation of deep learning methods in the educational process has gained immense popularity. The most successful among them are models that consider the multimodal nature of information, in particular the combination of text, sound, images, and video. The difficulty in processing such data is that combining multimodal input data by different channel concatenation methods that ignore the heterogeneity of different modalities is an inefficient approach. To solve this problem, an inter-channel attention module is proposed in this paper. The paper presents a computer vision-linguistic system of student learning process based on the concatenation of multimodal input data using the inter-channel attention module. It is shown that the creation of effective and flexible learning systems and technologies based on such models allows to adapt the educational process to the individual needs of students and increase its efficiency.