AZTUProgrammes

Subject · Environmental engineering

Modeling of ecological systemsTopics

İF-3087y5 creditsSpring semesterMandatory2025-2026

Topic plan

The subject's topics and the learning outcomes attached to each one.

36 topics

  1. 1. Topic: 2 classification of mathematical models applied in ecological systems

    Lecture

    Forms of modeling, physical modeling, analog modeling, intuitive modeling, signal modeling, physical and mathematical modeling

    Topic learning outcomes

    • Explains the nature of mathematical modeling in ecological systems and its role in solving environmental problems. distinguishes the main classification of mathematical models (deterministic, stochastic, static, dynamic, discrete, continuous, empirical and mechanistic models). compares the advantages and limitations of different model types.
    Open resource: Topic: 2 classification of mathematical models applied in ecological systems (opens in a new tab)

  2. 2. Topic: 3 application of ecological systems and models

    Lecture

    Composition and functions of ecosystems, ecosystem dynamics, basics of ecological models, application of ecosystem models

    Topic learning outcomes

    • Explains the structure, components and principles of operation of ecological systems. defines the areas of application of mathematical models used in the study of ecological systems. chooses a suitable model for solving various environmental problems and justifies its choice.
    Open resource: Topic: 3 application of ecological systems and models (opens in a new tab)

  3. 3. Topic: 4 economic-mathematical modeling process and classification

    Lecture

    General information about the economic-mathematical modeling process, functions of the modeled system, capabilities of the modeled system

    Topic learning outcomes

    • Explains the nature, purpose and application areas of economic-mathematical modeling. it describes the main stages of the economic-mathematical modeling process (problem definition, model construction, parameter selection, solution, verification and analysis of results). distinguishes the main classification of economic-mathematical models (deterministic, stochastic, static, dynamic, linear, non-linear, discrete and continuous models).
    Open resource: Topic: 4 economic-mathematical modeling process and classification (opens in a new tab)

  4. 4. Topic: 5 general information about the system concept. systematic approach

    Lecture

    Concept of system and its important features, division of models into classes according to application areas, systematic analysis and its stages

    Topic learning outcomes

    • Explains the concept of the system, its main features and elements. differentiates types of systems (open, closed, static, dynamic, simple and complex systems). it explains the essence, principles and importance of a systematic approach.
    Open resource: Topic: 5 general information about the system concept. systematic approach (opens in a new tab)

  5. 5. Topic: 6 identification of technological processes and technological system

    Lecture

    General information on the identification of technological processes, the main directions for studying chemical-technological processes, a chemical technological object is usually under the influence of various factors

    Topic learning outcomes

    • Explains the essence, purpose and importance of identification of technological processes. describes the concept of a technological system, its structure and main components. it explains the stages of identification of technological processes (data collection, model selection, parameter estimation and model verification).
    Open resource: Topic: 6 identification of technological processes and technological system (opens in a new tab)

  6. 6. Topic: 7 the main directions of building mathematical models

    Lecture

    Collection of primary data, construction of mathematical models of chemical technological processes, passive and active experimental methods of setting up the experiment depending on the order of collection of basic statistical materials

    Topic learning outcomes

    • It explains the purpose, essence and basic principles of building mathematical models. distinguishes the main directions of building mathematical models (analytical, statistical, experimental, simulation and optimization approaches). describes the stages of model building (problem formulation, hypothesis determination, selection of variables and parameters, model formulation, verification and improvement).
    Open resource: Topic: 7 the main directions of building mathematical models (opens in a new tab)

  7. 7. Topic: 8 the role of the computer in the modeling process

    Lecture

    The use of the computer in the modeling process and its important role, stages of computer (simulation) modeling, universal instrumental means of creating models

    Topic learning outcomes

    • Explains the role and importance of computer technologies in the modeling process. defines the software tools used in the construction, calculation and analysis of mathematical models. describes the stages of computer-based modeling (data entry, model building, simulation, processing and visualization of results).
    Open resource: Topic: 8 the role of the computer in the modeling process (opens in a new tab)

  8. 8. Topic: 9 static and dynamic mathematical models

    Lecture

    Economic-mathematical modeling process and its essence, classification of economic-mathematical methods, division of economic-mathematical models into static and dynamic models according to the time factor

    Topic learning outcomes

    • Explains the nature, properties and application fields of static and dynamic mathematical models. identifies and compares the main differences between static and dynamic models. he chooses the appropriate type of model for solving various problems and justifies his choice.
    Open resource: Topic: 9 static and dynamic mathematical models (opens in a new tab)

  9. 9. Subject: 10 areas of application of economic-mathematical methods

    Lecture

    Application of economic-mathematical methods, purpose in models of real economic systems, development of a mathematical model, mathematical analysis of the model, data structure and algorithm development

    Topic learning outcomes

    • Explains the essence, purpose and importance of economic-mathematical methods. defines the main areas of application of economic-mathematical methods (economics, management, finance, logistics, production, marketing and risk management). chooses a suitable mathematical method for solving various economic problems and justifies its choice.
    Open resource: Subject: 10 areas of application of economic-mathematical methods (opens in a new tab)

  10. 10. Topic: 11mathematical model of industrial waste water purification processes from metal ions

    Lecture

    Absorption treatment of waste water, sorption dynamics model, complete mathematical model of sorption dynamics in non-equilibrium mode

    Topic learning outcomes

    • Explains the impact of metal ions contained in industrial waste water on the environment. it distinguishes the main methods of metal ion removal processes (chemical precipitation, adsorption, ion exchange, membrane technologies, etc.). explains the principles of building mathematical models of metal ion purification processes.
    Open resource: Topic: 11mathematical model of industrial waste water purification processes from metal ions (opens in a new tab)

  11. 11. Topic: 12 environmental problems of the oil industry

    Lecture

    Sources of oil pollution of the sea and the effect of oil on living organisms, modeling of the process of spreading oil and oil products in the sea, methods of combating oil pollution, mathematical models of the process of spreading oil in the sea

    Topic learning outcomes

    • It explains the impact of the oil industry on the environment and the main environmental problems. it identifies the sources of pollution arising during oil production, processing and transportation. analyzes the effects of oil industry on soil, water, atmosphere and living world.
    Open resource: Topic: 12 environmental problems of the oil industry (opens in a new tab)

  12. 12. Topic: 13 methods of combating oil pollution and modeling the process of spreading oil in the sea

    Lecture

    Causes of sea water pollution with oil and oil products, methods of combating oil pollution, mathematical models of the process of spreading oil into the sea

    Topic learning outcomes

    • Explains the causes of oil pollution and its effects on marine ecosystems. differentiates oil pollution control methods (mechanical, physical, chemical and biological methods) and explains their application features. it determines the main factors affecting the spread of oil in the sea (wind, wave, current, temperature and physico-chemical properties of oil).
    Open resource: Topic: 13 methods of combating oil pollution and modeling the process of spreading oil in the sea (opens in a new tab)

  13. 13. Topic: 14 modeling the process of soil pollution with oil

    Lecture

    Reasons for soil pollution with oil, mathematical model of the process of oil seepage into the soil, mathematical model of the process of spreading oil on the earth's surface

    Topic learning outcomes

    • It explains the causes of soil oil pollution and its impact on the environment. identifies the main factors (soil type, porosity, humidity, temperature and physico-chemical properties of oil) that affect the spread and migration of oil in the soil. explains the principles of mathematical modeling of the process of soil pollution with oil
    Open resource: Topic: 14 modeling the process of soil pollution with oil (opens in a new tab)

  14. 14. Topic: 15 landscape ecology and land use modeling

    Lecture

    Landscape ecology, land use impact on ecosystems, land use modeling

    Topic learning outcomes

    • Explains the nature of landscape ecology, its main concepts and research objects. defines the role of mathematical models in land use planning and management. analyzes landscape structure, functions and ecological processes.
    Open resource: Topic: 15 landscape ecology and land use modeling (opens in a new tab)

  15. 15. Topic: 16 modeling of agriculture and water resources

    Lecture

    Fields of application of agricultural models, main directions of modeling of water resources, application of integrated models

    Topic learning outcomes

    • Explains the nature and importance of mathematical modeling in agriculture and water resources management. identifies the main factors affecting agricultural production and use of water resources. distinguishes the main mathematical models used in the modeling of water balance, irrigation systems and agricultural processes.
    Open resource: Topic: 16 modeling of agriculture and water resources (opens in a new tab)

  16. 16. Topic: 17 biogeography and species distribution models

    Lecture

    The role of various factors in the spread of species, the dynamics and model of the spread of species, the effect of climate change on ecosystems

    Topic learning outcomes

    • Explains the nature, purpose and basic concepts of biogeography. determines the natural and anthropogenic factors affecting the geographical distribution of living species. distinguishes the main mathematical models and methods used in species distribution modeling.
    Open resource: Topic: 17 biogeography and species distribution models (opens in a new tab)

  17. 17. Topic: 18 population models

    Lecture

    Concept of population, verhulst model in population, malthus model and population, ecological, elemental and human population

    Topic learning outcomes

    • Explains the nature, purpose and role of population models in ecological systems. it identifies the main factors affecting population dynamics (birth, death, migration, resources and environmental factors). distinguishes the main mathematical models describing population growth (exponential, logistic and other population models).
    Open resource: Topic: 18 population models (opens in a new tab)

  18. 18. Topic: 19 population growth models

    Lecture

    Exponential growth model, logistic growth model, natural resource management, stochastic growth model

    Topic learning outcomes

    • Explains the nature, purpose and application areas of population growth models. identifies the main factors affecting population growth (birth, death, migration, resource limitations, and environmental factors). distinguishes the main mathematical models describing population growth (exponential, logistic and other growth models).
    Open resource: Topic: 19 population growth models (opens in a new tab)

  19. 19. Topic: 20 models of interspecies interaction

    Lecture

    Types of interactions between species, parasitism and mutualism, commensialism and predation

    Topic learning outcomes

    • Explains the nature, types and ecological importance of interspecies interactions. it distinguishes interspecific relationships such as competition, predator-prey, parasite-host and mutualism. explains the basic mathematical models (lotka–volterra and other ecological models) that describe interspecies interactions.
    Open resource: Topic: 20 models of interspecies interaction (opens in a new tab)

  20. 20. Topic: 21 ecosystem dynamics and stability

    Lecture

    In this topic, concepts of the structure, dynamics and stability of ecosystems, biotic and abiotic factors affecting the functioning of ecosystems, assessment of ecosystem stability, mathematical modeling of ecological processes, prediction of ecosystem changes and the role of modeling in ensuring sustainable development are studied.

    Topic learning outcomes

    • Explains the essence, basic concepts and ecological importance of ecosystem dynamics and stability. identifies biotic and abiotic factors that affect the structure and dynamics of ecosystems. distinguishes the main mathematical models and methods used in the study of ecosystem dynamics.
    Open resource: Topic: 21 ecosystem dynamics and stability (opens in a new tab)

  21. 21. Topic: 23 modeling of local and global ecosystems

    Lecture

    Modeling at the local level, modeling of global ecosystems

    Topic learning outcomes

    • Explains the nature, characteristics and differences of local and global ecosystems. distinguishes the main mathematical models and methods used in modeling local and global ecosystems. identifies biotic, abiotic, and anthropogenic factors that influence ecosystem modeling.
    Open resource: Topic: 23 modeling of local and global ecosystems (opens in a new tab)

  22. 22. Topic: 1 concept of models in ecological systems, their classification and application

    Seminar

    This subject studies simplified mathematical or graphical representation — models — of ecological processes (population dynamics, energy flow, pollution spread). within the scope of the topic, the functions of models, their classification according to their complexity (conceptual, simulation, predictive models) and the practical application areas of these models for making decisions in environmental management are investigated.

    Topic learning outcomes

    • Explains the concept of the model, its essence and role in the study of ecological systems. distinguishes the main classification of models used in ecological systems (conceptual, physical, mathematical, deterministic, stochastic, static and dynamic models). chooses the appropriate type of model for solving environmental problems and justifies its choice.
    Open resource: Topic: 1 concept of models in ecological systems, their classification and application (opens in a new tab)

  23. 23. Topic: 2 economic-mathematical modeling process, application areas and identification of technological processes

    Seminar

    This subject covers the application of mathematical methods in the management of production, economy and technological processes. within the scope of the topic, the stages of economic-mathematical model construction (problem setting, variable selection, equation system formulation, analysis), their application areas in strategic planning and identification of technological processes — i.e., the methods of building a mathematical model of a real system based on input and output parameters are considered.

    Topic learning outcomes

    • Explains the essence, purpose and main stages of economic-mathematical modeling. defines the areas of application of economic-mathematical models (economy, management, production, logistics, ecology, etc.). explains the essence and basic principles of identification of technological processes.
    Open resource: Topic: 2 economic-mathematical modeling process, application areas and identification of technological processes (opens in a new tab)

  24. 24. Topic: 3 the main directions of building mathematical-static and mathematical-dynamic models and the role of the computer in modeling

    Seminar

    This subject covers the application of mathematical methods in the management of production, economy and technological processes. within the scope of the topic, the stages of economic-mathematical model construction (problem setting, variable selection, equation system formulation, analysis), their application areas in strategic planning and identification of technological processes — i.e., the methods of building a mathematical model of a real system based on input and output parameters are considered.

    Topic learning outcomes

    • Explains the nature, properties and application fields of static and dynamic mathematical models. defines the main stages and directions of building mathematical models. compares the differences between static and dynamic models and selects the appropriate model type for different problems.
    Open resource: Topic: 3 the main directions of building mathematical-static and mathematical-dynamic models and the role of the computer in modeling (opens in a new tab)

  25. 25. Topic: 4 environmental problems of the oil industry and mathematical models of industrial waste water purification process from metal ions

    Seminar

    This topic covers the anthropogenic effects of the oil and gas industry on the environment (soil, water, atmosphere) and the process of neutralization of water containing heavy metals, which is a special waste of this industry. in the topic, sources of pollution arising during oil extraction and processing, kinetic and dynamic mathematical models of cleaning metal ions (for example, pb 2+ , cu 2+ , cr 6+ ) from the water environment by sorption, ion exchange or precipitation methods are analyzed.

    Topic learning outcomes

    • Explains the main environmental problems of the oil industry and their impact on the environment. it determines the environmental risks of metal ions contained in industrial wastewater. it explains the methods of purification of metal ions from waste water and the principles of mathematical modeling of these processes.
    Open resource: Topic: 4 environmental problems of the oil industry and mathematical models of industrial waste water purification process from metal ions (opens in a new tab)

  26. 26. Topic: 6 biogeography and species distribution models population growth models

    Seminar

    This topic describes the patterns of geographical distribution of living organisms and their number dynamics. the biogeography section examines species distribution ranges, environmental factors (climate, topography, competition) that influence their location, and distribution models (eg, the theory of "island biogeography"). in the part of population growth models, how the number of living things changes over time — exponential (unlimited) and logistic (limited by the capacity of the environment) growth models is explained through mathematical equations.

    Topic learning outcomes

    • Explains the essence of biogeography, its basic concepts and the factors affecting the geographical distribution of species. distinguish between the main mathematical models that describe the distribution of species and population growth. identifies biotic, abiotic and anthropogenic factors affecting population growth.
    Open resource: Topic: 6 biogeography and species distribution models population growth models (opens in a new tab)

  27. 27. Topic: 7 interspecies interaction models, ecosystem dynamics and stability

    Seminar

    This topic explains the interaction of organisms within the ecosystem (predator-prey, competition, symbiosis) with mathematical models. here, through classical models such as "lotka-volterra" equations, the number dynamics of species, how the ecosystem changes over time (succession) and self-regulation against external influences (stability) are analyzed.

    Topic learning outcomes

    • Explains the nature, basic concepts and ecological importance of interspecies interactions and ecosystem dynamics. distinguish between interspecific relationships such as competition, predator-prey, parasite-host, and mutualism and evaluate their impact on the ecosystem. explains the basic mathematical models used in modeling interspecies interactions and ecosystem dynamics.
    Open resource: Topic: 7 interspecies interaction models, ecosystem dynamics and stability (opens in a new tab)

  28. 28. Topic: 8 simulation of ecosystem processes, modeling of local and global ecosystems

    Seminar

    This topic involves the creation of digital copies of complex processes occurring in ecosystems (carbon cycle, food chain, climate change). the simulation acts as a "digital laboratory" in situations where it is difficult or dangerous to conduct real environmental experiments. it compares the scale, data requirements, and predictive capabilities of local models (eg, the pollution dynamics of a lake or forest massif) and global models (eg, changes in earth's average temperature and biome migration).

    Topic learning outcomes

    • It explains the essence, purpose and application areas of the simulation of ecosystem processes and local-global ecosystem modeling. distinguishes the main mathematical and computer models used in the simulation of ecosystem processes. identifies biotic, abiotic, and anthropogenic factors that influence the modeling of local and global ecosystems.
    Open resource: Topic: 8 simulation of ecosystem processes, modeling of local and global ecosystems (opens in a new tab)

  29. 29. Topic: 1 definition, types, classification and application of models in ecological systems

    Independent work

    This topic covers the representation of ecological processes (population dynamics, energy flow, material circulation, etc.) in mathematical, graphical or physical forms, the nature, types and application of these models in the management of real ecosystems. ecological modeling is a key tool for simplifying complex natural phenomena and transforming them into manageable parameters.

    Topic learning outcomes

    • Explains the concept of the model, its essence and role in the study of ecological systems. distinguishes the main types and classification of models used in ecological systems (conceptual, physical, mathematical, deterministic, stochastic, static and dynamic models). selects the appropriate type of model for the study of ecological systems and justifies its choice.
    Open resource: Topic: 1 definition, types, classification and application of models in ecological systems (opens in a new tab)

  30. 30. Topic: 2 economic-mathematical static and dynamic modeling process and systematic approach

    Independent work

    This topic covers the expression of complex economic and ecological processes with quantitative indicators, the influence of the time factor on the models, and the investigation of the interrelationships between the elements of the system as a single mechanism. economic-mathematical modeling plays the role of scientific reasoning in decision-making.

    Topic learning outcomes

    • Explains the nature, purpose and characteristics of static and dynamic models of economic-mathematical modeling. identifies and compares the main differences between static and dynamic mathematical models. it explains the main stages of the economic-mathematical modeling process (setting the problem, building the model, selecting parameters, solving, checking and analyzing the results).
    Open resource: Topic: 2 economic-mathematical static and dynamic modeling process and systematic approach (opens in a new tab)

  31. 31. Topic: 3 environmental problems of the oil industry and a mathematical model of industrial waste water purification processes from metal ions

    Independent work

    This topic covers the anthropogenic impacts of the oil and gas sector on the environment (soil, water, air), especially the danger of heavy metals present in industrial wastewater to the ecosystem and the optimization of these water treatment technologies through mathematical models.

    Topic learning outcomes

    • Explains the main environmental problems of the oil industry and their impact on the environment. it identifies the environmental and human health risks posed by metal ions in industrial wastewater. it explains the main methods of metal ion removal processes and the principles of mathematical modeling of these processes.
    Open resource: Topic: 3 environmental problems of the oil industry and a mathematical model of industrial waste water purification processes from metal ions (opens in a new tab)

  32. 32. Topic: 4 methods of combating oil pollution of land and sea water, modeling of oil pollution of sea water and land

    Independent work

    This topic covers the physical, chemical and biological treatment technologies applied during oil spills, as well as mathematical modeling approaches that predict the dynamics of the spread of this pollution.

    Topic learning outcomes

    • It explains the causes of oil pollution of land and sea water, the mechanisms of its spread and its impact on the environment. distinguishes the main methods of combating oil pollution (mechanical, physical, chemical and biological methods) and explains their application characteristics. identifies the main factors affecting the spread of oil in seawater and land and analyzes their influence on the process.
    Open resource: Topic: 4 methods of combating oil pollution of land and sea water, modeling of oil pollution of sea water and land (opens in a new tab)

  33. 33. Topic: 5 agricultural and water resource modeling of biogeography and species distribution

    Independent work

    This topic includes the analysis of the patterns of geographic distribution of living organisms (biogeography), as well as the optimization through mathematical models of agricultural productivity and the management of water resources, which are critical to human activity. these systems are important for ensuring ecological resilience in the face of climate change and anthropogenic impacts.

    Topic learning outcomes

    • Explains basic concepts of biogeography, patterns of geographic distribution of species, and the role of modeling in agriculture and water resource management. identifies biotic, abiotic, and anthropogenic factors affecting species distribution, agricultural production, and water resource status. distinguishes the main mathematical models and methods used in the modeling of species distribution, agriculture and water resources.
    Open resource: Topic: 5 agricultural and water resource modeling of biogeography and species distribution (opens in a new tab)

  34. 34. Topic: 22 simulation of ecosystem processes

    Lecture

    This topic covers the study of natural processes occurring in ecosystems through computer models and simulation methods. during the simulation, interactions between living things (predator-prey relationships, competition, symbiosis), population dynamics, energy flow, substance circulation and the effect of environmental factors on the ecosystem are modeled. within the framework of the topic, various scenarios are established and changes that may occur in ecosystems are predicted, the role of simulation in making scientifically based decisions for the management of natural resources and the protection of biodiversity is studied. also, the skills of analyzing environmental processes using mathematical modeling, system dynamics and computer programs are formed.

    Topic learning outcomes

    • Explains the concept of simulation of ecosystem processes. it defines the main components of the ecosystem and their interrelationships. it models ecological processes such as population dynamics, energy flow, and material cycling.
    Open resource: Topic: 22 simulation of ecosystem processes (opens in a new tab)

  35. 35. Topic: 1 concept of model in ecological systems and its types

    Lecture

    Ekoloji sistemlərdə modelləşdirmə və onun əhəmiyyəti, model anlayışı və onun növləri, modelləşdirmə haqqında ümumi məlumat və onun mahiyyəti

    Topic learning outcomes

    • Explains the concept of a model and explains the role of a model in scientific research. it explains the nature of the ecological model and its importance in the study of the environment. defines the main characteristics of ecological systems (complexity, interaction, dynamics, etc.).
    Open resource: Topic: 1 concept of model in ecological systems and its types (opens in a new tab)

  36. 36. Topic: 5 methods of combating oil pollution of sea waters and land, modeling of land use, agriculture and water resources.

    Seminar

    This topic combines two major directions: 1) environmental cleaning technologies and 2) digital modeling of resource management. physical (barriers, mechanical collection), chemical (dispersants) and biological (bioremediation) methods of combating oil pollution of the marine and land environment are considered. at the same time, the methods of building and optimizing mathematical models for the productivity of agricultural fields, soil erosion, irrigation systems and the dynamics of underground/surface water resources are analyzed.

    Topic learning outcomes

    • Explains the causes and environmental consequences of oil pollution of sea waters and land. differentiates the methods of combating oil pollution (mechanical, physical, chemical and biological methods) and evaluates their advantages and disadvantages. explains the principles of modeling the spread of oil spills and understands the importance of forecasting.
    Open resource: Topic: 5 methods of combating oil pollution of sea waters and land, modeling of land use, agriculture and water resources. (opens in a new tab)