Experimental Studies of the Digital Twin of Plant based on Ontologies

and Multi-Agent Technologies

PETR SKOBELEV1, ALEKSEY TABACHINSKIY1, ANATOLY STRIZHAKOV1,

EVGENY KUDRYAKOV1, ELENA SIMONOVA2

Samara Federal Research Scientific Center RAS,

3a Studencheskiy Lane, 443001, Samara,

RUSSIA

2Institute of Informatics and Cybernetics,

Samara National Research University,

34 Moskovskoye Shosse, 443086, Samara,

RUSSIA

Abstract: - The article discusses the results of research achieved in the field of developing an intelligent digital

twin of plants (DTP). An ontological model of the crop production process is proposed, and expanded by

including descriptions of physiological and technological factors: predecessors in crop rotation, seed

reproduction, and consumption of macro-elements from the soil. The multi-agent DTP model has been

modified to account for the morphological and physiological characteristics of crop varieties, as well as

parameters for each phenological phase of the plant. A software prototype of the DTP is presented,

implementing the developed methods for simulating the production process of crop plants. Experimental

cultivation of crops using the DTP was conducted in the 2022/2023 season. The obtained datasets during the

experiments will be used to calibrate the model and improve the accuracy of predicting plant parameters at each

phenological phase.

Key-Words: - precision agriculture, smart farming, digital twin of plants, crop variety model, multi-agent

technology, knowledge base, ontology.

Received: April 27, 2024. Revised: September 18, 2024. Accepted: October 19, 2024. Published: November 22, 2024.

1 Introduction

The transition to the digitalization of all sectors of

the economy, including agriculture, is of particular

interest to researchers of mathematical models and

artificial intelligence methods. The principles of

precision farming, whose achievement will

significantly increase the efficiency of crop

cultivation, are based on a set of digital technologies

related to the collection and processing of data,

autonomous decision-making for field works, and

control of their implementation, [1], [2]. Every year,

the use of digital twins in agriculture is expanding,

primarily covering systems that simulate specific

aspects of the business process of plant cultivation,

[3]. Systems for simulation parameters of the

production process are also known from scientific

sources; however, these solutions are of early

technological readiness primarily.

One reason is that the processes involved in

plant cultivation are much more complex compared

to manufacturing and require the integration of

multidisciplinary knowledge in physics and

chemistry, biology, agronomy, soil science, and

several other fields. Another challenge is adaptive

planning and simulation of plant growth based on

unpredicted rapidly changing external factors.

Additionally, it involves developing precise

recommendations that can help farmers and

agronomists to timely implement the required field

works specifically in the location and time. Finally,

the production process of the virtual plant must be

synchronized with the growth of real plants through

timely diagnosis of crop parameters of the real

plants.

In this regard, the task of creating a digital twin

of plants (DTP) becomes relevant, allowing to

determine the timing and predicted indicators of

crop growth under given environmental conditions,

which is necessary for precision farming. The

concept of the DTP, developed in this article, is

based on the application of an ontologically

configurable multi-agent system (MAS), [4], [5].

This system allows for real-time planning and

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DOI: 10.37394/232015.2024.20.60

Petr Skobelev, Aleksey Tabachinskiy,

Anatoly Strizhakov, Evgeny Kudryakov,

Elena Simonova

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simulation of the production process of crops,

characterized by dynamically changing

compositions and quantities of input data. Some of

this data can be expressed through refined expert

assessments provided by agronomists.

The article has the following structure. The first

chapter discusses the task of digitalization in

precision farming. The second chapter provides a

general overview of the digital twins for

the simulation of plant growth stages. The third

chapter gives an overview of existing solutions in

the field of using models for the production process

of plants and justifies the need for developing new

approaches based on interdisciplinary knowledge.

The fourth chapter describes variety and resource

models within the ontology of plant cultivation. The

fifth chapter justifies the development of the multi-

agent DTP model by introducing agents of the

morphological features of plants. The sixth chapter

examines the architecture and functions of the DTP

prototype. The seventh chapter describes an

experiment on wheat cultivation using the DTP. The

eighth chapter discusses the outcomes of the

developments and prospects for the further

advancement of the DTP.

2 The Concept of the Digital Twin of

Plants

The current research on developing digital twins of

agricultural crops has been conducted since 2021 in

collaboration with several agricultural research

institutions. These are utilized in decision support

systems for managing resources in agricultural

enterprises. The authors define the concept of

the "Digital twin of plants" as an intelligent system

for planning and simulating the growth and

development of plant crops based on environmental

data. This system regularly synchronizes with real

plants during the production process, [6]. The

classes of agents necessary for describing the DT of

crops are presented in Table 1.

At the core of DTP implementation lies an

ontological approach to represent knowledge in the

subject domain, enabling the construction of a

knowledge base (KB) of stages of development for

various plant varieties in the form of a semantic

network of instances of concept classes and

relationships. Subsequently, this knowledge can be

supplemented and refined from the experience

accumulated by specialists during the cultivation of

specific crops.

The process of plant development is described

through a sequence of successive stages with

predetermined rules for determining their duration

and calculating indicators of plant development. The

rules for calculating the duration of stages and

indicators of plant development are based on a

simplified mathematical model that sets ranges of

environmental parameter values for each stage:

under normal plant development trajectories, as well

as in the event of hazardous weather phenomena

(such as frost, prolonged absence of precipitation,

etc.) and exceeding critical boundaries. If the

parameter value falls within acceptable limits, a

linear law of stage duration change and penalties for

monitored plant indicators, such as yield, is applied.

When exceeding the permissible boundaries, the

maximum possible penalty is assigned. In addition

to boundary values for calculation rules, the

penalties for exceeding the established boundaries

depend on the duration of the parameter exceeding

these boundaries.

Table 1. Classes of agents of the DT of plant crops

Agent class

Functions

plant agent as a

whole

coordinates the work of other agents

stage agents

define the needs of the plant at each

stage

agents of

resources and

growth

opportunities

are refined at each stage based on

data from sensors, external services,

or agronomists

parts of the plant

agents

operate within each stage and are

responsible for decision-making at

their level

agronomist agent

generates context-dependent

recommendations for plant

cultivation following the evolving

situation

environment

agent

provides data on weather and

environmental conditions from

sensors and meteorological services

The effects of different parameters can be

combined using various aggregation strategies: sum

or multiplication, and selection of the minimum or

maximum value. Changes in environmental

parameters (such as weather or soil conditions) at

any stage should trigger an adaptive recalculation of

the duration and indicators of plant development for

that stage and subsequent stages.

In the MAS of the DTP, several levels of

representation of the production process of plants

are developed, but the primary one is the multi-

agent network of needs and capabilities (NC-

network). It is linked to the stages of plant growth

and development, capturing their resource

requirements and resource availability. Within this

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approach, agents operate within an internal virtual

market with the capability to buy and sell time slots

in the schedule. Agents can identify issues and

resolve conflicts by applying negotiation protocols

and a compensation method based on individual

satisfaction functions (SF), as well as bonuses and

penalties, [6].

DTP enables the calculation and prediction of

the date and duration of growth and development

stages, the length of the vegetation period, and the

quantity and quality of the harvest based on weather

and soil data. Additionally, it incorporates

observations and analyses conducted in both field

and laboratory conditions. The forecasting of the

harvest and other indicators is performed based on a

variety of model constructed in touch with the soil-

climatic conditions of the cultivation zone, as well

as the biological and morphological characteristics

of the crop. The variety model is filled with

information in the form of functional dependencies

of crop parameters.

The MAS of the DTP is extended to calculate a

dynamic set of crop parameters (multi-parameter

model) as well as rules for resource

replenishment/expenditure in the external

environment. This significantly enhances the

simulation accuracy when confirmed data on

resource consumption and expenditure in the soil

are available.

The purpose of this article is to present the

results achieved in the development of the DTP and

to describe the experimental cultivation of crops

using the DTP during the 2022/2023 season.

3 State of the Art

One of the most challenging tasks in implementing

DT for plant cultivation is the development of a

production model for plant that is dependent on

external environmental factors.

Paper [7] explores mathematical models of the

growth of agricultural crops based on algebraic or

differential equations. They calculate variable rates

(photosynthesis, leaf area expansion, etc.) and state

variables (crop biomass, yield, etc.) at each stage of

plant development throughout the vegetative period

based on the crop status, soil conditions, and

weather. However, such models often turn out to be

complex and are only implementable in relatively

simple cases, covering a small portion of the tasks.

Simulation models forecast changes in the state

of agricultural crops over time based on exogenous

parameters. The AGROTOOL system describes the

fundamental processes in the agroecosystem "soil-

plant-atmosphere" from sowing to full maturity, [8].

However, even for the initial run, the model must

contain data for the past 5–6 years of vegetation.

Moreover, simulation models are not directly linked

to the real object and are not synchronized with its

changes.

Paper [9] proposes a "digital prototype" of a

crop to account for individual soil-climatic

conditions and plant needs within a comprehensive

system for precision agriculture. This system

includes digital platforms, artificial intelligence (AI)

programs, feedback sensors, and tools for preparing

and precisely delivering balanced fertilizers,

micronutrients, and plant protection agents at the

right time, in the specified location, and in the

required quantities.

Paper [10] explores the Digital Twin project

Virtual Tomato Crops (VTC), which includes a 3D

simulation model predicting tomato yield based on

the utilization of nutrients, lighting, and water. The

foundation of VTC is a Functional-Structural Plant

Model (FSPM) that simulates internal processes in

plants, including light capture, photosynthesis in

leaves, assimilate distribution, leaf area growth, and

stem elongation.

With the transition to Agriculture 4.0, there is

an increasing demand for industry-specific solutions

to optimize production processes. In this context,

digital twins are most widely represented for

greenhouse farming, [11], [12]. However, digital

twins for open-field plant cultivation are still in the

early stages of development, [13], [14].

The review [15] found that digital twin

technology is expanding its influence in agriculture.

However, future studies should pay much attention

to the characteristics of living organisms and their

twinning with virtual entities. The authors also state

that the architecture of digital twins for crop

cultivation should be further enhanced, as should its

functionality.

The analysis of research in the field of digital

agriculture has revealed that currently there are no

solutions that allow for the simulation of the

comprehensive state of a crop based on real-time

environmental data and provide forecasts of its

condition throughout the major vegetative stages

until the harvest. Some individual solutions are

capable of calculating specific parameters, such as

forecasted yield, under limited conditions. The

insufficient level of development of digital tools in

this field is associated with the complexity of the

problem, which requires the simulation of biological

systems based on the integration of interdisciplinary

knowledge.

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4 Ontological Models of the

Production Process of Plants

Within the research, an ontological model of the

production process was developed, encompassing

variety and resource models. This model allows

modifications to the plant variety model, including

the composition and applicability conditions of

growth rules, without reprogramming the DTP. This

flexibility is useful for accommodating new

agronomic or technological factors and cultures of

crops.

Different crops go through various stages of

development throughout their life cycle according to

the BBCH scale [16], each characterized by specific

conditions for transitioning to the next stage. By

using a graph depicting the interconnection of

parameters between the plant stages, the sequential

development of plants during the vegetative period

from one stage to the next can be represented. This

graph defines which parameters in the next stage are

affected by the parameters from the previous stage

(Figure 1). Quantity estimation of this correlation is

declared in the variety model, which is described

later.

Fig. 1: Fragment of the parameter graph for the

growth and development stages of winter wheat

4.1 The Variety Model

The variety model consists of an array of "tubes" for

all output parameters applicable at a specific stage.

Each "tube" describes the reaction of one output

parameter from one input parameter (factor) at a

particular stage and its “depth” of plant reaction.

The tube of parameters includes critical and optimal

ranges for the input parameter, which describe

different plant behavior (reaction). DTP estimates

the reaction for each input parameter and aggregates

them to calculate the value of each affected output

parameter of the plant, [6]. The array of input

parameter ranges, the depths of variety reaction to

each of the factors, and other variety-specific rules

together form a variety model. Such rules include

the ripening group, the nominal duration of the life

cycle, a list of resources, and their influence on the

affected parameters of the plant throughout its life

cycle.

A fragment of the ontological model of the

variety (using winter wheat as an example),

including functional dependencies of a series of

output parameters on the factor "Soil moisture at the

0-10 cm level," is presented in Table 2.

Table 2. A fragment of the class "Variety model" of

the ontology

Soil cont.,

Critical

max

Secondary

root system

Stem

length, cm

Number of

leaves, pcs

Optim.

Critical

min

The variety model takes into account the

genetic and technological features of the plant

production process:

- the influence of predecessors in crop rotation on

the duration of growth stages and yield is

achieved by imposing penalties on similar

characteristics if the predecessor is fallow;

- the impact of seed reproduction on yield is

achieved through penalties based on the planned

yield, applied to the biological yield rate;

- the influence of environmental factors (such as

temperature and air humidity) on the duration of

plant development is accounted for by using

correction coefficients applied to the calculated

deviation value of the plant development stage

duration;

- stage-wise extraction of macro-elements

(nitrogen, phosphorus, potassium, or NPK) from

the soil.

The growth and development of plants occur

through the utilization of resources. The duration of

a stage is determined by the rate of plant

development, which depends on the suitability of

external environmental conditions, determined by

the plant's satisfaction function with the level of

specific resources and the totality of resources.

4.2 The Resource Model

The resource has the following characteristics:

initial actual value at the sowing date, expenditure

rule, replenishment rule, and current value. The

influence of resources on plant parameters at

different stages is described in the variety model in

the form of:

- resource boundary points (tubes). One tube

describes the influence of one resource on one

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output parameter of the plant: critical minimum,

recommended value (optimum), critical

maximum;

- values of the affected output parameters at the

boundary points;

- expert rules in case the critical minimum is not

reached or the critical maximum is exceeded.

At this stage of implementing the DTP, the

following resources are taken into account: average

daily air temperature, soil moisture at several levels

(0-10; 0-30; 0-100 cm depending on the stage of

plant development and root system depth), relative

humidity, and nutrient reserves in the soil in the

form of NPK.

The current resource value is calculated based

on the actual resource volume at the initial moment

(date of planting) and rules for its expenditure and

replenishment. The current value of the resource

may be periodically updated based on data provided

by the agronomist, which they input during the

synchronization mode of the DTP, for instance, after

receiving laboratory soil analysis results.

The accounting of resources in the DTP model

is based on the actual growth and development

strategy of the plant (the crop response to daily

changes in external conditions) according to the

methodology described in the authors' work, [6].

Specifically, accounting for the influence of the

prioritized factor for plant growth, such as air

temperature, is carried out using two parameters: the

sum of active temperatures and the plant's

satisfaction function with temperature. The stage

agent calculates the daily value of the plant's SF

based on the temperature value depending on which

interval of the variety model's tube the temperature

value falls into (Figure 2).

Accordingly, the values of the SF (YT) can range

from 0 to 1:

- T  [Tmin, Tcr_min), YT is calculated according

to a rule RuleL, determined by the agronomist,

plant death is possible;

- T  [Tcr_min, Trec_min], penalty YT is

calculated according to the linear dependence;

- T [Trec_min, Trec_max], YT =1, no

bonus/penalty is awarded;

- T  [Trec_max, Tcr_max], bonus YT is

calculated according to the linear dependence;

- T [Tcr_max, Tmax], YT is calculated

according to a rule RuleR, determined by the

agronomist, plant death is possible.

The obtained duration value of the stage and the

reason for the deviation (if any) are communicated

by the stage agent to the plant agent. As a result, the

plant agent receives the calculation of the duration

of each stage and deviations in the development of

the crop throughout the entire vegetation cycle.

Simultaneously with the duration of stages, the

DTP calculates the values of output parameters of

the crop (yield, etc.) depending on the available

resources.

Fig. 2: The form of the satisfaction function of the

stage agent in relation to the magnitude of the

resource (air temperature)

5 The Development of the Multi-

Agent Multi-Parametric Model of

the Digital Twin of Plants

The state of the DTP  at each stage of growth

and development is determined by a combination of

three factors:

  󰇝  󰇞

where – ontological model of plant, P – the

constructed plan of plant growth and development,

KPI – the comprehensive indicator of stage

progression efficiency.

Let   be the state of a real plant,

 – the

state of the DTP. The accuracy of the DTP model

will be high if the difference between the states of

the real plant and its DTP at each moment in time k

is minimal:



 

 ,

where  – function determining the difference

between the indicators of the DT with the

parameters of the real plant.

In case of a new event  occurring on a real

field in the farm, the DTP should move to a new

state as quickly as possible by rescheduling the

stages affected by the event:



  

 ,

where  – function adaptively reconfigures the plant

growth plan in response to the occurred event.

In this study, the concept of a multi-level multi-

agent model of the DTP was developed. This model

incorporates both horizontal and vertical

interactions among agents, leading to the emergence

of a "collective intelligence" of the plant, which has

an emergent nature, [17]. The agent world

architecture in MAS of DTP includes the following

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types of agents: fields, plants (crops), stages, and

resources, as well as the plant agent as a whole. The

MAS is created according to a hierarchical

principle, where the top-level agent is the plant

agent, and the agents of stages and resources, which

are responsible for directly regulating the plant

growth process, are located at the lower level.

Initially, agents of plant growth stages and resource

agents are created. The stage agents start working

sequentially. Resource agents correspond to the

input parameters of the environment.

In this case, the NC-network of the DTP

represents a network of agents of plant growth

stages and resource agents, which adaptively

recalculate in a chain, and form a "competitive

equilibrium" based on data from meteorological

stations and results of field inspections by

agronomists. The plant agent as a whole, observing

the calculation results, can adjust the parameters of

the tubes for each stage of plant growth and

development, influencing the conservation or,

conversely, the expedited utilization of the

corresponding resource.

The world of MAS agents is supplemented with

agents representing plant morphological

characteristics (height, leaf area, root length, and

area, stem diameter and height, etc.) and

physicochemical parameters of crops (chlorophyll,

protein, carbohydrates, water, temperature, macro-

and micronutrients N, P, K, Ca, S, Cu, Zn). To

implement the level of plant morphological

characteristics in the DTP, complementing the

simulation of stages, an approach presented in

Figure 3 is proposed, where an "organ agent" is

introduced – a type of agent representing plant

morphological characteristics. The list of specific

"organ agents" for each crop is described in the KB

using logical rules for the appearance of the organ

and a mathematical model of its functioning,

represented as functions of its influence on various

aspects of the plant's production process. Further

introduction to the multiagent world of DTP is

provided in [6] and other previous papers of the

authors.

Fig. 3: Decomposition of stage agents in the MAS

of DTP

6 Architecture and Functions of the

DTP Prototype

The main subsystems of the DTP prototype include

an ontology/knowledge base constructor for

describing classes of concepts and relationships, as

well as domain-specific rules necessary for DTP

calculations, and a multi-agent subsystem for

planning and simulating plant growth and

development. Each of these subsystems contains

client and server parts. Additionally, there is a

mobile application for phones and tablets running

on the Android operating system.

The client part, implemented in JavaScript with

the Vue framework, utilizing CSS/HTML markup,

enables the DTP user to work through a website

accessible from any internet browser. The web

application implements functions for creating,

modifying, and deleting objects of the following

classes: Users, Fields, Crops, Calculation results of

crops, Journal entries of crops (synchronization),

Virtual crops, and fields.

The software interface of the web application

provides functions:

- retrieving a list of fields, as well as a list of

crops in the field with the ability to sort by field,

crop, variety, and season;

- creating a crop on a field with user-specified

planting parameters;

- creating a simulated crop as a virtual copy of the

real one;

- building temporal diagrams of external

environmental factors based on field

environment parameter data;

- constructing a Gantt chart of the growth and

development plan of the crop based on DTP

calculations;

- creating a journal entry for the crop

synchronization function.

The determination of environmental factors and

soil indicators is carried out through the interaction

of the DTP with the KAIPOS intelligent weather

monitoring systems. The data obtained from the

weather station is used to create an environmental

parameter source, which provides calculations of 5-

year averages for each parameter throughout the

year. Subsequently, a long-term forecast of

parameters is generated, enabling the prediction of

the crop conditions for future dates.

The server part, implemented in Java, is

intended for conducting calculations and interacting

with external services and includes subsystems:

- subsystem of ontology and knowledge base

constructor for crops;

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- multi-agent subsystem for planning and

simulation of plant growth and development, as

well as forecasting crop yield and generating

recommendations;

- data visualization subsystem;

- data storage subsystem (database);

- subsystem of communication with users;

- subsystem for integration with weather services

and other sensors.

The methodological aspects of the organization

and algorithm of the DTP prototype's functioning

are described in more detail in the authors' previous

articles. The growth and development plan of the

plant constructed in the DTP represents the

sequence and parameters of stages. Changing the

value of a parameter on a specific date through

synchronization with real crops leads to the

recalculation of all related parameters in the growth

and development stage scheduler of the DTP's

MAS. This, in turn, affects all subsequent stages and

may alter the forecast of crop quantity or quality.

7 Experimental Cultivation of Wheat

using DTP in the 2022/2023 Season

Crop fields have coordinates, technological maps,

crop rotation history, agronomist observation plans,

and other data. The experimental validation of the

DTP was conducted by comparing the results of

DTP calculations with the actual conditions of

different wheat varieties and predecessors grown in

the Middle Volga region. The diagrams (Figure 4)

illustrate deviations in the duration of stages

obtained as a result of DTP calculations for various

crops. The calculation is based on the environmental

and crop data, such as air temperature and humidity,

precipitation, available soil moisture (Figure 5) and

soil content (NPK), stem height, plant mass

throughout the growing season (Figure 6), leaf

surface area, and several others.

In particular, significant deviations were

recorded in the initial DTP calculations for soft

winter wheat varieties. Subsequently, with each

subsequent synchronization, the interval decreased.

Synchronizations conducted after the earing stage

show that the deviation intervals do not exceed 5

days in magnitude. The calculations of the

development of hard spring wheat demonstrate a

relatively low deviation interval in the negative

direction, not exceeding 7 days. A significant (in

magnitude) deviation of up to 16 days is observed

during synchronization at the flowering stage,

caused by a misinterpreted rule for transitioning to

the milk ripeness phase, which introduces "chain-

by-chain" deviations into the development scenarios

of subsequent phases.

Based on the experimental cultivation of the

2022/2023 season using DTP, the following main

results were obtained:

1. Based on the discrepancies between planned

and actual indicators in the DTP, adjustments to

the growth and development rules, as well as

variety model values, were made;

2. The average accuracy of predicting the duration

of stages for all crops is 93.2% for the entire

vegetation period and 99% for the Earing stage;

3. The experimental cultivation methodology for

the 2022/2023 season has been refined in terms

of specifying parameters of factor satisfaction

functions, which will increase the accuracy of

DTP forecasting for the data of the 2024 season.

Fig. 4: Difference between the DTP-calculated and

actual vegetation duration

Fig. 5: Diagram of the soil moisture

Fig. 6: Diagram of actual plant mass

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8 Conclusion

In the presented study, the ontological model of

crop production for DTP has been expanded to

include crop rotation predecessors, seed

reproductions, soil content consumption, and some

other environmental factors. The multi-agent model

of the production process in DTP has been modified

to account for a multitude of input and output

parameters of plant crop conditions. For each stage,

a resource model has been introduced, allowing for

determining the influence of discrepancies between

resource requirements and their actual availability

on the output parameters of plant conditions. The

software implementation of the DTP prototype has

been completed.

The experimental research has provided a

dataset for calibrating the DTP crop model and

improving the accuracy of forecasting plant

parameters at each stage. The system functionality

will be expanded across various crops for product

application (soybeans, corn, potatoes), as well as

including a DTP-based subsystem for generating

recommendations for agronomists on crop

management technologies in different regions.

References:

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Anatoly Strizhakov, Evgeny Kudryakov,

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

- Petr Skobelev has proposed the multiagent

method to solve the problem and supervised the

research. -Aleksey Tabachinskiy has developed

the wheat knowledge base and managed the

experimental validation.

- Anatoly Strizhakov has provided the agronomical

knowledge and conducted the experimental study.

- Evgeny Kudryakov is responsible for DTP

interaction and testing, which allowed to provide

all DTP calculations.

- Elena Simonova set up state-of-the-art research,

analysed the DTP results as compared to the real

crops, composed and edited the paper summary.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

This study was funded by the grant of Russian

Science Foundation № 22-41-08003,

https://rscf.ru/project/22-41-08003/.

Conflict of Interest

The authors have no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

_US

WSEAS TRANSACTIONS on ENVIRONMENT and DEVELOPMENT

DOI: 10.37394/232015.2024.20.60

Petr Skobelev, Aleksey Tabachinskiy,

Anatoly Strizhakov, Evgeny Kudryakov,

Elena Simonova

E-ISSN: 2224-3496

632

Volume 20, 2024