One-step Stochastization Methods for Open Systems

Korolkova, Anna V.; Kulyabov, Dmitry S.

doi:10.1051/epjconf/202022602014

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…For further analysis of the qualitative properties of the models, we study the influence of stochastics introduction. For this purpose, it is proposed to develop a stochastic model by constructing self-consistent stochastic models [13,30,32,43,44]. This method involves, in the course of mathematical transformations, obtaining the coefficients of the Fokker-Planck equation from the interaction scheme, which allows implementing a symbolic record of all possible interactions in the system.…”

Section: Construction Of Stochastic Models "Two Competitorstwo Migrat...mentioning

confidence: 99%

“…For multidimensional models, the simplest linear models with additive noise are most often used, however, this approach does not fully take into account stochastic processes in the system. A promising direction is stochastic modeling of dynamic systems based on the method of constructing self-consistent one-step models [30][31][32]. Using this method, we can perform an algorithmic transition to a stochastic model and evaluate the influence of stochastics on the qualitative properties of the model.…”

Section: Introductionmentioning

confidence: 99%

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Construction, stochastization and computer study of dynamic population models “two competitors - two migration areas”

Vasilyeva

Demidova

Druzhinina³

et al. 2023

Discrete and Continuous Models

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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.

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Section: Construction Of Stochastic Models "Two Competitorstwo Migrat...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Construction, stochastization and computer study of dynamic population models “two competitors - two migration areas”

Vasilyeva

Demidova

Druzhinina³

et al. 2023

Discrete and Continuous Models

View full text Add to dashboard Cite

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Development of Algorithms and Software for Modeling Controlled Dynamic Systems Using Symbolic Computations and Stochastic Methods

Demidova

Druzhinina

Masina

et al. 2023

Program Comput Soft

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Development of Algorithms and Software for Modeling Controlled Dymamic Systems Using Symbolic Computations and Stochastic Methods

DEMIDOVA,

DRUZHININA,

MASINA

et al. 2023

Programmirovanie

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The development of software for synthesizing and analyzing models of controlled systems taking into account their deterministic and stochastic description is an important direction of research. Results of the development of software for modeling dynamic systems the behavior of which can be described by onestep processes are presented. Models of population dynamics are considered as an example. The software uses a deterministic description of the model at its input to obtain a corresponding stochastic model in symbolic form and also analyze the model in detail (calculate trajectories in the deterministic and stochastic cases, find control functions, and visualize the results). An important aspect of the development is the use of computer algebra for analyzing the model and synthesizing controls. Methods and algorithms based on deterministic and stochastic Runge–Kutta methods, stability and control theory, methods for designing self-consistent stochastic models, numerical optimization algorithms, and artificial intelligence are implemented. The software was developed using high-level programming languages Python and Julia. As the basic tools, high-performance libraries for vector–matrix computations, symbolic computation libraries, libraries for the numerical solution of ordinary differential equations, and libraries of global optimization algorithms are used.

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One-step Stochastization Methods for Open Systems

Abstract: In this paper, two approaches (combinatorial and operatorial) to the stochastization of the one-step processes are discussed for the closed and open version of the Lotka–Volterra model, respectively.

Cited by 3 publications

References 13 publications

Construction, stochastization and computer study of dynamic population models “two competitors - two migration areas”

Construction, stochastization and computer study of dynamic population models “two competitors - two migration areas”

Development of Algorithms and Software for Modeling Controlled Dynamic Systems Using Symbolic Computations and Stochastic Methods

Development of Algorithms and Software for Modeling Controlled Dymamic Systems Using Symbolic Computations and Stochastic Methods

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