Synthesis and Analysis of Multidimensional Mathematical Models of Population Dynamics

Demidova, Anastasia V.; Druzhinina, O. V.; Jacimovic, Milojica; Masina, Olga N.; Mijajlović, Nevena

doi:10.1109/icumt.2018.8631252

Cited by 4 publications

(4 citation statements)

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“…Population dynamic models are characterized by the fact that when describing them, it is necessary to take into account various types of interaction in the population community, for example, intraspecific competition, interspecific competition, trophic interactions, migration, mutualism [16][17][18]. For example, research is being conducted related to the study of the properties of multidimensional ecological and demographic systems, taking into account competition and migration flows [19][20][21][22]. As the results show, the impact of migration can be significant, and the presence of migration flows leads to the emergence of new qualitative effects.…”

Section: Introductionmentioning

confidence: 99%

“…When constructing models, migration mechanisms are described using linear and nonlinear functions [15,[24][25][26]. The stability and qualitative behavior of population-migration models are considered in [18,24,[26][27][28][29] and other papers. Despite a number of interesting results in the direction of studying systems with migration flows, there is a need to construct and research new models with migration.…”

Section: Introductionmentioning

confidence: 99%

“…When studying high-dimensional models, the choice of parameters can be carried out by applying evolutionary algorithms [12,[33][34][35]. Various systems of population dynamics (with competition, mutualism, migration) based on self-consistent models are considered in [12,14,28] and other papers.…”

Section: Introductionmentioning

confidence: 99%

“…The three-dimensional model "predator-prey-one migration area" is considered in [29]. Four-dimensional population models with competition and one area of migration are studied in [20,41]. This article is devoted to the study of such a four-dimensional population model of the type "two competitorstwo migration areas", which takes into account changes in the reproduction rates of populations.…”

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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