Pub Date : 2023-09-30DOI: 10.22363/2658-4670-2023-31-2-139-149
M. Gevorkyan, A. Korolkova, D. Kulyabov
This article discusses a universal way to create animation using Asymptote the language for vector graphics. The Asymptote language itself has a built-in library for creating animations, but its practical use is complicated by an extremely brief description in the official documentation and unstable execution of existing examples. The purpose of this article is to eliminate this gap. The method we describe is based on creating a PDF-file with frames using Asymptote, with further converting it into a set of PNG images and merging them into a video using FFmpeg. All stages are described in detail, which allows the reader to use the described method without being familiar with the used utilities.
{"title":"Asymptote-based scientific animation","authors":"M. Gevorkyan, A. Korolkova, D. Kulyabov","doi":"10.22363/2658-4670-2023-31-2-139-149","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-2-139-149","url":null,"abstract":"This article discusses a universal way to create animation using Asymptote the language for vector graphics. The Asymptote language itself has a built-in library for creating animations, but its practical use is complicated by an extremely brief description in the official documentation and unstable execution of existing examples. The purpose of this article is to eliminate this gap. The method we describe is based on creating a PDF-file with frames using Asymptote, with further converting it into a set of PNG images and merging them into a video using FFmpeg. All stages are described in detail, which allows the reader to use the described method without being familiar with the used utilities.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46941193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.22363/2658-4670-2023-31-3-242-246
Olga V. Babourova, Boris N. Frolov
The curvature tensor (hat{R}) of a manifold is called harmonic, if it obeys the condition (Delta^{text{(HR)}}hat{R}=0), where (Delta^{text{(HR)}}=DD^{ast} +
D^{ast}D) is the Hodge–deRham Laplacian. It is proved that all solutions of the Einstein equations in vacuum, as well as all solutions of the Einstein–Cartan theory in vacuum have a harmonic curvature. The statement that only solutions of Einstein’s equations of type (N) (describing gravitational radiation) are harmonic is refuted.
{"title":"Hodge-de Rham Laplacian and geometric criteria for gravitational waves","authors":"Olga V. Babourova, Boris N. Frolov","doi":"10.22363/2658-4670-2023-31-3-242-246","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-3-242-246","url":null,"abstract":"The curvature tensor (hat{R}) of a manifold is called harmonic, if it obeys the condition (Delta^{text{(HR)}}hat{R}=0), where (Delta^{text{(HR)}}=DD^{ast} +
 D^{ast}D) is the Hodge–deRham Laplacian. It is proved that all solutions of the Einstein equations in vacuum, as well as all solutions of the Einstein–Cartan theory in vacuum have a harmonic curvature. The statement that only solutions of Einstein’s equations of type (N) (describing gravitational radiation) are harmonic is refuted.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135886008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.22363/2658-4670-2023-31-3-247-259
Eduardo L. André, Alexander N. Tsirulev
We propose an efficient method for Hamiltonian simulation of multi-qubit quantum systems with special types of interaction. In our approach, the Hamiltonian of a (n)-qubit system should be represented as a linear combination of the standard Pauli basis operators, and then decomposed into a sum of partial Hamiltonians, which are, in general, not Pauli operators and satisfy some anticommutation relations. For three types of Hamiltonians, which are invariant with respect to permutations of qubits, the effectiveness of the main algorithm in the three-qubit cluster model is shown by calculating the operator exponentials for these Hamiltonians in an explicit analytical form. We also calculate the density operator, partition function, entropy, and free energy of the cluster weakly coupled to a thermal environment. In our model, the cluster is in the Gibbs state in the temperature interval (0.1!-!2:!text{K}), which corresponds to the operating range of modern quantum processors. It follows from our analysis that the thermodynamic properties of such systems strongly depend on the type of internal interaction of qubits in the cluster.
{"title":"Hamiltonian simulation in the Pauli basis of multi-qubit clusters for condensed matter physics","authors":"Eduardo L. André, Alexander N. Tsirulev","doi":"10.22363/2658-4670-2023-31-3-247-259","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-3-247-259","url":null,"abstract":"We propose an efficient method for Hamiltonian simulation of multi-qubit quantum systems with special types of interaction. In our approach, the Hamiltonian of a (n)-qubit system should be represented as a linear combination of the standard Pauli basis operators, and then decomposed into a sum of partial Hamiltonians, which are, in general, not Pauli operators and satisfy some anticommutation relations. For three types of Hamiltonians, which are invariant with respect to permutations of qubits, the effectiveness of the main algorithm in the three-qubit cluster model is shown by calculating the operator exponentials for these Hamiltonians in an explicit analytical form. We also calculate the density operator, partition function, entropy, and free energy of the cluster weakly coupled to a thermal environment. In our model, the cluster is in the Gibbs state in the temperature interval (0.1!-!2:!text{K}), which corresponds to the operating range of modern quantum processors. It follows from our analysis that the thermodynamic properties of such systems strongly depend on the type of internal interaction of qubits in the cluster.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135886899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.22363/2658-4670-2023-31-3-260-272
Kouame A. Brou
Since the appearance of COVID-19, a huge amount of data has been obtained to help understand how the virus evolved and spread. The analysis of such data can provide new insights which are needed to control the progress of the epidemic and provide decision-makers with the tools to take effective measures to contain the epidemic and minimize the social consequences. Analysing the impact of medical treatments and socioeconomic factors on coronavirus transmission has been given considerable attention. In this work, we apply panel autoregressive distributed lag modelling (ARDL) to European Union data to identify COVID-19 transmission factors in Europe. Our analysis showed that non-medicinal measures were successful in reducing mortality, while strict isolation virus testing policies and protection mechanisms for the elderly have had a positive effect in containing the epidemic. Results of Dumitrescu-Hurlin paired-cause tests show that a bidirectional causal relationship exists for all EU countries causal relationship between new deaths and pharmacological interventions factors and that, on the other hand, some socioeconomic factors cause new deaths when the reverse is not true.
{"title":"Identification of COVID-19 spread factors in Europe based on causal analysis of medical interventions and socio-economic data","authors":"Kouame A. Brou","doi":"10.22363/2658-4670-2023-31-3-260-272","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-3-260-272","url":null,"abstract":"Since the appearance of COVID-19, a huge amount of data has been obtained to help understand how the virus evolved and spread. The analysis of such data can provide new insights which are needed to control the progress of the epidemic and provide decision-makers with the tools to take effective measures to contain the epidemic and minimize the social consequences. Analysing the impact of medical treatments and socioeconomic factors on coronavirus transmission has been given considerable attention. In this work, we apply panel autoregressive distributed lag modelling (ARDL) to European Union data to identify COVID-19 transmission factors in Europe. Our analysis showed that non-medicinal measures were successful in reducing mortality, while strict isolation virus testing policies and protection mechanisms for the elderly have had a positive effect in containing the epidemic. Results of Dumitrescu-Hurlin paired-cause tests show that a bidirectional causal relationship exists for all EU countries causal relationship between new deaths and pharmacological interventions factors and that, on the other hand, some socioeconomic factors cause new deaths when the reverse is not true.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135886895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.22363/2658-4670-2023-31-3-273-281
Eugeny Yu. Shchetinin
This paper investigates neurotechnologies for developing brain-computer interaction (BCI) based on the generative deep learning Stable Diffusion model. An algorithm for modeling BCI is proposed and its training and testing on artificial data is described. The results are encouraging researchers and can be used in various areas of BCI, such as distance learning, remote medicine and the creation of robotic humanoids, etc.
{"title":"Brain-computer interaction modeling based on the stable diffusion model","authors":"Eugeny Yu. Shchetinin","doi":"10.22363/2658-4670-2023-31-3-273-281","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-3-273-281","url":null,"abstract":"This paper investigates neurotechnologies for developing brain-computer interaction (BCI) based on the generative deep learning Stable Diffusion model. An algorithm for modeling BCI is proposed and its training and testing on artificial data is described. The results are encouraging researchers and can be used in various areas of BCI, such as distance learning, remote medicine and the creation of robotic humanoids, etc.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135886006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.22363/2658-4670-2023-31-3-228-241
Evgeniy B. Laneev, Obaida Baaj
The paper proposes a stable method for constructing a normal to a surface given approximately. The normal is calculated as the gradient of the function in the surface equation. As is known, the problem of calculating the derivative is ill-posed. In the paper, an approach is adopted to solving this problem as to the problem of calculating the values of an unbounded operator. To construct its stable solution, the principle of minimum of the smoothing functional in Morozov’s formulation is used. The normal is obtained in the form of a Fourier series in the expansion in terms of eigenfunctions of the Laplace operator in a rectangle with boundary conditions of the second kind. The functional stabilizer uses the Laplacian, which makes it possible to obtain a normal in the form of a Fourier series that converges uniformly to the exact normal vector as the error in the surface definition tends to zero. The resulting approximate normal vector can be used to solve various problems of mathematical physics using surface integrals, normal derivatives, simple and double layer potentials.
{"title":"On a stable calculation of the normal to a surface given approximately","authors":"Evgeniy B. Laneev, Obaida Baaj","doi":"10.22363/2658-4670-2023-31-3-228-241","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-3-228-241","url":null,"abstract":"The paper proposes a stable method for constructing a normal to a surface given approximately. The normal is calculated as the gradient of the function in the surface equation. As is known, the problem of calculating the derivative is ill-posed. In the paper, an approach is adopted to solving this problem as to the problem of calculating the values of an unbounded operator. To construct its stable solution, the principle of minimum of the smoothing functional in Morozov’s formulation is used. The normal is obtained in the form of a Fourier series in the expansion in terms of eigenfunctions of the Laplace operator in a rectangle with boundary conditions of the second kind. The functional stabilizer uses the Laplacian, which makes it possible to obtain a normal in the form of a Fourier series that converges uniformly to the exact normal vector as the error in the surface definition tends to zero. The resulting approximate normal vector can be used to solve various problems of mathematical physics using surface integrals, normal derivatives, simple and double layer potentials.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135886892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.22363/2658-4670-2023-31-3-218-227
Aleksandr A. Belov, Igor V. Gorbov
Solutions of many applied Cauchy problems for ordinary differential equations have one or more multiple zeros on the integration segment. Examples are the equations of special functions of mathematical physics. The presence of multiples of zeros significantly complicates the numerical calculation, since such problems are ill-conditioned. Round-off errors may corrupt all decimal digits of the solution. Therefore, multiple zeros should be treated as special points of the differential equations. In the present paper, a local solution transformation is proposed, which converts the multiple zero into a simple one. The calculation of the latter is not difficult. This makes it possible to dramatically improve the accuracy and reliability of the calculation. Illustrative examples have been carried out, which confirm the advantages of the proposed method.
{"title":"Numerical integration of the Cauchy problem with non-singular special points","authors":"Aleksandr A. Belov, Igor V. Gorbov","doi":"10.22363/2658-4670-2023-31-3-218-227","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-3-218-227","url":null,"abstract":"Solutions of many applied Cauchy problems for ordinary differential equations have one or more multiple zeros on the integration segment. Examples are the equations of special functions of mathematical physics. The presence of multiples of zeros significantly complicates the numerical calculation, since such problems are ill-conditioned. Round-off errors may corrupt all decimal digits of the solution. Therefore, multiple zeros should be treated as special points of the differential equations. In the present paper, a local solution transformation is proposed, which converts the multiple zero into a simple one. The calculation of the latter is not difficult. This makes it possible to dramatically improve the accuracy and reliability of the calculation. Illustrative examples have been carried out, which confirm the advantages of the proposed method.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135886893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.22363/2658-4670-2023-31-3-205-217
Anatoly A. Nazarov, Svetlana V. Rozhkova, Ekaterina Yu. Titarenko
The mathematical model of the retrial queuing system (M^{[n]}/M/1) with feedback and batch Poisson arrival is constructed. Customers arrive in groups. If the server is free, one of the arriving customers starts his service, the rest join the orbit. The retrial and service times are exponentially distributed. The customer whose service is completed leaves the system, or reservice, or goes to the orbit. The method of asymptotic diffusion analysis is proposed for finding the probability distribution of the number of customers in orbit. The asymptotic condition is growing average waiting time in orbit. The accuracy of the diffusion approximation is obtained.
{"title":"Asymptotic diffusion analysis of the retrial queuing system with feedback and batch Poisson arrival","authors":"Anatoly A. Nazarov, Svetlana V. Rozhkova, Ekaterina Yu. Titarenko","doi":"10.22363/2658-4670-2023-31-3-205-217","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-3-205-217","url":null,"abstract":"The mathematical model of the retrial queuing system (M^{[n]}/M/1) with feedback and batch Poisson arrival is constructed. Customers arrive in groups. If the server is free, one of the arriving customers starts his service, the rest join the orbit. The retrial and service times are exponentially distributed. The customer whose service is completed leaves the system, or reservice, or goes to the orbit. The method of asymptotic diffusion analysis is proposed for finding the probability distribution of the number of customers in orbit. The asymptotic condition is growing average waiting time in orbit. The accuracy of the diffusion approximation is obtained.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135886898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-30DOI: 10.22363/2658-4670-2023-31-1-46-63
K.A. Brou, I. V. Smirnov
Foreign direct investment (FDI) can have a significant impact on economic development in developing economies like Russia. FDI can bring in capital, technology, and management expertise that can stimulate economic growth, increase employment, and improve productivity. In the case of Russia, FDI has played a vital role in the country’s economic development. A study conducted by the World Bank in 2019 found that FDI inflows have contributed significantly to Russia’s economic growth and led to increased productivity, employment, and exports. The article analyzes the relationship between foreign direct investment and economic growth in Russia using ARDL cointegration and Toda-Yamamoto causality analysis test. The results reveal that there is no causality relation between GDP growth and foreign direct investment inflow in Russia. Overall, foreign direct investment effectively contributes to economic growth in Russia in the short term and not really in the long run.
{"title":"Causality relationship between foreign direct investments and economic improvement for developing economies: Russia case study","authors":"K.A. Brou, I. V. Smirnov","doi":"10.22363/2658-4670-2023-31-1-46-63","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-1-46-63","url":null,"abstract":"Foreign direct investment (FDI) can have a significant impact on economic development in developing economies like Russia. FDI can bring in capital, technology, and management expertise that can stimulate economic growth, increase employment, and improve productivity. In the case of Russia, FDI has played a vital role in the country’s economic development. A study conducted by the World Bank in 2019 found that FDI inflows have contributed significantly to Russia’s economic growth and led to increased productivity, employment, and exports. The article analyzes the relationship between foreign direct investment and economic growth in Russia using ARDL cointegration and Toda-Yamamoto causality analysis test. The results reveal that there is no causality relation between GDP growth and foreign direct investment inflow in Russia. Overall, foreign direct investment effectively contributes to economic growth in Russia in the short term and not really in the long run.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42013206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-30DOI: 10.22363/2658-4670-2023-31-1-27-45
I. I. Vasilyeva, A. V. Demidova, O. Druzhinina, O. Masina
When studying deterministic and stochastic population models, the actual problems are the formalization of processes, taking into account new effects caused by the interaction of species, and the development of computer research methods. Computer research methods make it possible to analyze the trajectories of multidimensional population systems. We consider the “two competitors - two migration areas” model, which takes into account intraspecific and interspecific competition in two populations, as well as bidirectional migration of both populations. For this model, we take into account the variability of the reproduction rates of species. A formalized description of the four-dimensional model “two competitors - two migration areas” and its modifications is proposed. Using the implementation of the evolutionary algorithm, a set of parameters is obtained that ensure the coexistence of populations under conditions of competition between two species in the main area, taking into account the migration of these species. Taking into account the obtained set of parameters, a positive stationary state is found. Two-dimensional and three-dimensional projections of phase portraits are constructed. Stochastization of the model “two competitors - two migration areas” is carried out based on the method of self-consistent one-step models constructing. The Fokker-Planck equations are used to describe the structure of the model. A transition to a four-dimensional stochastic differential equation in the Langevin form is performed. To carry out numerical experiments, a specialized software package is used to construct and study stochastic models, and a computer program based on differential evolution is developed. Algorithms for generating trajectories of the Wiener process and multipoint distributions and modifications of the Runge-Kutta method are used. In the deterministic and stochastic cases, the dynamics of the trajectories of populationmigration systems is studied. A comparative analysis of deterministic and stochastic models is carried out. The results can be used in modeling of different classes of dynamic systems.
{"title":"Construction, stochastization and computer study of dynamic population models “two competitors - two migration areas”","authors":"I. I. Vasilyeva, A. V. Demidova, O. Druzhinina, O. Masina","doi":"10.22363/2658-4670-2023-31-1-27-45","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-1-27-45","url":null,"abstract":"When studying deterministic and stochastic population models, the actual problems are the formalization of processes, taking into account new effects caused by the interaction of species, and the development of computer research methods. Computer research methods make it possible to analyze the trajectories of multidimensional population systems. We consider the “two competitors - two migration areas” model, which takes into account intraspecific and interspecific competition in two populations, as well as bidirectional migration of both populations. For this model, we take into account the variability of the reproduction rates of species. A formalized description of the four-dimensional model “two competitors - two migration areas” and its modifications is proposed. Using the implementation of the evolutionary algorithm, a set of parameters is obtained that ensure the coexistence of populations under conditions of competition between two species in the main area, taking into account the migration of these species. Taking into account the obtained set of parameters, a positive stationary state is found. Two-dimensional and three-dimensional projections of phase portraits are constructed. Stochastization of the model “two competitors - two migration areas” is carried out based on the method of self-consistent one-step models constructing. The Fokker-Planck equations are used to describe the structure of the model. A transition to a four-dimensional stochastic differential equation in the Langevin form is performed. To carry out numerical experiments, a specialized software package is used to construct and study stochastic models, and a computer program based on differential evolution is developed. Algorithms for generating trajectories of the Wiener process and multipoint distributions and modifications of the Runge-Kutta method are used. In the deterministic and stochastic cases, the dynamics of the trajectories of populationmigration systems is studied. A comparative analysis of deterministic and stochastic models is carried out. The results can be used in modeling of different classes of dynamic systems.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42902828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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