Methods Of Mathematical Modeling Research Articles

Optimal Control Problems in Complex Systems: The Combination of Mathematical Modeling and Optimization Strategies

Optimal control in complex systems is a challenging and practical field. Traditional control methods can not meet the needs of complex systems, so mathematical modeling and optimization strategies are needed to improve system performance and stability. The optimal control theory can solve the control problem in complex system effectively and improve the operation efficiency of the system by establishing mathematical model and combining optimization strategy. From mathematical modeling method to hybrid optimization strategy research, this paper discusses the theory and practice of optimal control in depth. In the future, it is necessary to further improve the research methods to solve the uncertainty of complex system models and make greater contributions to realizing more intelligent control schemes.

A Systematic Review of Modeling and Simulation for Precision Diamond Wire Sawing of Monocrystalline Silicon.

Precision processing of monocrystalline silicon presents significant challenges due to its unique crystal structure and chemical properties. Effective modeling and simulation are essential for advancing the understanding of the manufacturing process, optimizing design, and refining production parameters to enhance product quality and performance. This review provides a comprehensive analysis of the modeling and simulation techniques applied in the precision machining of monocrystalline silicon using diamond wire sawing. Firstly, the principles of mathematical analytical model, molecular dynamics, and finite element methods as they relate to monocrystalline silicon processing are outlined. Subsequently, the review explores how mathematical analytical models address force-related issues in this context. Molecular dynamics simulations provide valuable insights into atomic-scale processes, including subsurface damage and stress distribution. The finite element method is utilized to investigate temperature variations and abrasive wear during wire cutting. Furthermore, similarities, differences, and complementarities among these three modeling approaches are examined. Finally, future directions for applying these models to precision machining of monocrystalline silicon are discussed.

Some aspects of consıderable models of oıl and gas ındustry development

The article examines some assumptions and problems of the world economic theory, it is pointed out that these assumptions are based on the characteristics of the economic structure in different parts of the world where the distribution of world production and the global exchange of goods, services and other results of human activity take place, of course the oil and gas industry is not left out in this matter shown. Moreover, taking into account the importance of its impact on world politics, it has been pointed out that the field is one of the most relevant objects of economic analysis today. The characteristic features of modern globalization are given in the article. In such a situation, it was suggested that since the real scale of the application of methods that increase oil production in Azerbaijan is not able to prevent the deterioration of the structure of reserves, it will not be possible to make a big positive change in the exploitation of extractable reserves. The article also discusses the application of econometric models in economic research on the oil and gas industry. As a means of research and prediction of natural processes, the mathematical modeling method has been shown to be very widespread in oil and gas extraction. The observations made were summarized and it was shown that there is a systematic progress in the dynamics of the world economic system in the conditions of modern globalization, the main characteristic features of modern globalization were classified and given by the author, the creation of optimal conditions for the operation of the oil and gas industry as a result of the administrative and fiscal regulation of the state in the conditions of globalization was noted, and also the oil and gas industry some aspects of the theoretical models of the future development of the field have been studied and shown, taking into account its specific characteristics and in the context of the natural decrease of the volume of production. In the article, it was determined that one of the most important issues is the correct determination of the oil and gas reserves of the field, its calculation by separate reserve categories. Experience shows that it is very important to calculate these resources in different ways, to analyze the indicators of field development in detail, and to compare them with real indicators in order to implement one or another project indicators. The basis of these methods is the determination of reserves and their role in the technical-economic justification of the options for field development. This gives special relevance to such issues in the oil and gas industry and considers their constant improvement in the conditions of the market economy appropriate. The developed article is dedicated to the study of such issues.

ИНФОРМАЦИЯЛЫК ТЕХНОЛОГИЯЛАРДЫ ОКУТУУДА МАТЕМАТИКАЛЫК МОДЕЛДИН ОРДУ

This paper discusses technologies for using mathematical modeling methods in teaching information technology. A method for selecting the types of problems to be solved using mathematical modeling and decision-making methods is proposed. Mathematical modeling makes it possible to present current information in a more compact, structured form, since mathematical formulas are designed to allow you to write the current problem in a more concise, understandable and memorable form. Another important area that can be used in educational projects is the assessment and calculation of alternative energy sources that are more efficient than the electricity used today. Of great interest is also the study of the dynamics of human reproduction in modern society. When implementing the above projects with the help of a computer, you can find a solution to the problem, create a simulation model and display a graphic image using software such as PowerSim.

Amur Tiger Individual Identification Based on the Improved InceptionResNetV2.

Accurate and intelligent identification of rare and endangered individuals of flagship wildlife species, such as Amur tiger (Panthera tigris altaica), is crucial for understanding population structure and distribution, thereby facilitating targeted conservation measures. However, many mathematical modeling methods, including deep learning models, often yield unsatisfactory results. This paper proposes an individual recognition method for Amur tigers based on an improved InceptionResNetV2 model. Initially, the YOLOv5 model is employed to automatically detect and segment facial, left stripe, and right stripe areas from images of 107 individual Amur tigers, achieving a high average classification accuracy of 97.3%. By introducing a dropout layer and a dual-attention mechanism, we enhance the InceptionResNetV2 model to better capture the stripe features of individual tigers at various granularities and reduce overfitting during training. Experimental results demonstrate that our model outperforms other classic models, offering optimal recognition accuracy and ideal loss changes. The average recognition accuracy for different body part features is 95.36%, with left stripes achieving a peak accuracy of 99.37%. These results highlight the model's excellent recognition capabilities. Our research provides a valuable and practical approach to the individual identification of rare and endangered animals, offering significant potential for improving conservation efforts.

Применение эволюционных и роевых методов для оптимизации многопараметрического управления процессом нанесения гальванического покрытия

One of the key parameters of the quality of ceramic coatings is its thickness, which must meet technical requirements and provide the necessary degree of corrosion protection, wear resistance and appearance of the coating. Ensuring the uniformity of the galvanic coating is one of the most important and complex tasks of high-tech machine-building production, for which a number of methods have been proposed, such as controlling current modes, the location of electrodes in the bath, and the electrolyte flow rate. However, in most cases, these methods require solving the problem of optimal multiparametric control. Prompt and accurate optimization when changing the conditions of electrolysis (electrode potentials, composition and properties of the electrolyte), as well as, if necessary, taking into account the multi-extreme nature of the dependence of the uniformity coefficient on the process parameters (current density, interelectrode distance, electrolyte flow rate) is a rather complex and ambiguous multifactorial task that limits the use of classical methods for- the claim of a global extreme. The article explores the possibility and expediency of using intelligent heuristic methods, such as evolutionary and swarm methods, to solve this problem. Objective. The objective of this study is to determine the effectiveness of using genetic algorithms and the particle swarm method to solve the problem of optimizing the multiparametric control of the electroplating process. Materials and methods. Methods of mathematical modeling, methods and software environment of numerical modeling and optimization were used to conduct the study. Results. The article investigates the effectiveness of the application of evolutionary and swarm optimization methods in relation to the process of applying chrome plating in a galvanic bath with many anodes with multiparametric control of current density, interelectrode distance and electrolyte flow rate. The best approximation to the extreme of the uniformity coefficient can be achieved by genetic algorithms using the mutation operation and the particle swarm method, while achieving the extreme using the particle swarm method is achieved in fewer iterations. Conclusion. The results of the study substantiate the expediency of using evolutionary and swarm methods to solve the problem of optimizing the multiparametric control of the electroplating process, while it is possible to increase the efficiency of these methods due to additional tuning.

Оценка альтернатив: новые подходы принятия решений в условиях определенности

The decision-making process plays an important role in the development of society in general and the effective management of organizations in particular. In today's world, where the complexity of tasks and the competitive environment are constantly growing, making the right and informed decisions becomes a key element of success. Any person, group of people or organization is constantly faced with the need to choose between several possible courses of action, called alternatives, whether in the personal sphere or in the work of organizations. To effectively make complex decisions within the activities of organizations, models for making optimal decisions have been developed. The most popular of them is the model of decision-making under conditions of certainty, when the outcome of the decision is not influenced by random factors. All this confirms the relevance of scientific research in the field of decision making. Aim. The purpose of the study is to develop a methodology for assessing the degree of attractiveness of alternatives based on objective quantitative or subjective qualitative criteria, which will improve the quality of decisions made. The methodology is based on mathematical models for processing information containing the characteristics of alternatives according to evaluation criteria. Materials and methods. The methodology for evaluating alternatives presented in the work is based on mathematical models of information processing, which are based on methods of mathematical modeling, optimization methods, linear programming, theory of fuzzy sets, theory of latent variables, as well as methods of decision-making under conditions of uncertainty and methods of expert assessment. Results. The relevance of the development of a model for evalua¬ting construction projects according to quantitative criteria is shown, ways of solving the tasks are given and justified. A mathematical model has been developed that makes it possible to evaluate construction projects by objective indicators based on the theory of fuzzy sets and the Rush model for estimating latent variables. On the basis of numerical methods, the adequacy of the received estimates of construction projects is substantiated, the methodology for implementing computational procedures necessary for the practical implementation of evaluation models is described. Conclusion. The application of the given methodology in the decision-making procedure under conditions of certainty will improve the quality of decisions made and reduce the risks of their implementation.

Multi-pose dress simulation of fully-fashioned knitted skirt based on loop structure

To realize the three-dimensional structure simulation and dress simulation of the fully-fashioned knitted skirt, based on the study of the structural characteristics of the fully-fashioned knitted skirt, the mathematical model of the knitted skirt pattern, the loop geometry mathematical model and the loop mesh model were established by the method of mathematical modelling. The spatial transformation relationship of each pair of triangles in the plate model and the three-dimensional surface model was calculated by using the spatial matrix. To draw a loop on the surface model's triangular patch, spatial transformation was used to calculate the grid point positions and obtain three-dimensional coordinates of the loop-type value points. Based on C# programming language, the human body model in the database was matched with the knitted skirt surface model, and the three-dimensional graphics library Open-GL and loop drawing method were used to realize the simulation of the knitted skirt dress based on the loop structure. The simulation method was tested by the dressing effects of hip skirts and umbrella skirts with different postures. The results showed that the spatial transformation could realize the fast transformation and calculate the coordinates of the loop-type value points. The C# programming language and Open-GL technologies realized the visual simulation of the fully-fashioned knitted skirt and the multi-pose dressing simulation based on the loop structure.

Mathematical modelling and control approach for sustainable ecosystems in mitigating the impact of pollutants on aquatic species in rivers

This paper focuses on the urgent issue of minimising the impact of pollutants on aquatic life in river ecosystems. Our innovative approach involves the integration of mathematical modelling and strategic control methods to counteract the negative consequences of industrial and agricultural activities. The model, developed in a one-dimensional context, captures the complex dynamics of species population and pollutant concentration. Using an optimisation framework, we strive to achieve a harmonious balance that limits pollution, enhances species diversity and optimises control expenditure. Ultimately, we seek to harmonise industrial progress with ecological vitality, promoting the sustainability of river ecosystems for generations to come.

Parametric Study of a Large Active Area PEM Fuel Cell using a MatLab-Simulink Model

A Matlab-Simulink based mathematical model and simulation method is developed by applying appropriate physics and electro-chemistry that adequately describes a proton exchange membrane fuel cell (PEMFC) system. The mathematical model is then simulated for a single low temperature PEMFC with a large, 350cm2, active area. The single cell’s performance was evaluated using different operating conditions and varying values of various crucial system parameters. The Matlab-Simulink model presented in this investigation is used to study various parameters’ effect such as the cell temperature from 50℃ to 90℃, inlet pressure, relative humidity (RH) from 70% to 90%, and the reactant stoichiometry ratio, on the cell performance. Comparison of polarization and power density curves were conducted between the model simulation and experimental data at 60℃ and at 65℃. Except for the higher current densities range (≥1.6 A/cm2), the simulation results match with the experimental results very well. The parametric study was used to determine the optimum value of various parameters. The fuel cell performance with the optimized parameter values show a good improvement using the developed MatLab-Simulink model.

Neural network model development for detecting atypical mitoses in histological slides

Background: Modern computer systems allow digitizing and examining images of histological preparations, which led the authors to the idea of using machine learning tools in digital pathohistology. The ability of neural networks to find sub-visual image features in digitized histological preparations provides the basis for better qualitative and quantitative image analysis. Existing machine learning methods provide good accuracy and speed in recognizing various images, which gives hope for their wide application, including in oncologic diagnostics. AIM: Use methods of mathematical modeling to identify pathological mitoses in histological preparations as the main sign of the difference between malignant and benign tumor growth. MATERIALS AND METHODS: Histological images of the N.N. Priorov National Medical Research Center of Traumatology and Orthopedics were used as a data set for the neural network model. The model was tested using 188 histologic slides from 67 patients treated at the institute. Histological preparations were scanned on a Leica Aperio CS2 microscope with a ×400 resolution and converted into JPEG format with further processing. Next, the test images were analyzed in streaming mode using the created neural network model in order to obtain the coordinates of the desired diagnostic object — pathological mitosis and the probability with which the model found the object of this category. The obtained images were analyzed by a pathologist to determine whether the detected object corresponded to pathological mitosis. RESULTS: The authors have chosen an architecture, developed a methodology for training a neural network, and created a model that can be used to detect pathologic mitoses in histologic preparations. The authors do not attempt to replace the physician, but show the possibility of an integrated approach to data analysis by a computer system and a pathologist. Conclusions: The developed mathematical model of neural network used as a part of technological solution for recognizing pathological mitoses in scanned histological preparations can be used as a tool to reduce the time of research and increase the accuracy of diagnosis by a pathologist.

Improving Cytogenetic Surveillance in Radiology Workers Exposed to Low-Dose Radiation in Africa: A Call to Action

Radiation exposure is an occupational hazard for diagnostic and interventional radiology workers, potentially leading to chromosomal damage and increased cancer risk. This review explores the status of cytogenetic monitoring of radiation exposure among radiology workers in Africa. Monitoring of Radiation Exposure in Diagnostic and Interventional Radiology Workers in Ghana and Africa provides a crucial examination of radiation safety practices within the Ghanaian and Africa healthcare sector. We recovered existing literature on the cytogenetic surveillance conducted on radiology workers in Ghana and Africa stressing on the impact and/or significance of cytogenetic monitoring programmes. In these studies, mostly mathematical modeling and physical methods were used to estimate and extrapolate risks of exposure to ionizing radiation. Additionally, we discuss the challenges and opportunities for implementing cytogenetic monitoring programmes in Africa particularly Ghana and provide recommendations for future research and occupational health policies. This review attempts to bridge the gap between physical and biological dosimetry in surveillance studies. It addresses the significant gap in cytogenetic monitoring among diagnostic and interventional radiology workers in Africa. It highlights the importance of cytogenetic surveillance for early detection of radiation-induced genetic damage, assesses the current practices, and provides a recommendation and a roadmap for establishing robust monitoring programmes. This work would contribute significantly to the understanding of occupational radiation safety issues in the healthcare sector of Africa. It also offers a comprehensive examination of the challenges and opportunities in implementing cytogenetic monitoring programmes.

Efficient mathematical methods for modeling and simulating adsorption of copper (II) on activated carbon utilizing date nuts

In our research, we demonstrate the application of mathematical methodologies to analyze the retention efficiency of Cu2+ cations through adsorption on powdered activated carbon derived from date nuts. Due to the growing importance of copper elimination in environmental spheres, there is a need for accurate simulation and prediction techniques. The investigation emphasizes the significance of numerical methods in improving simulation precision. The integration of optimization strategies and numerical approaches offers a comprehensive predictive framework for copper adsorption on activated carbon. By utilizing initial parameters as inputs, the Matlab algorithm proposed by Hassouna in this study is employed to simulate the adsorption mechanisms, with the resultant outputs encompassing the nature of adsorption (isotherms, kinetics). The findings results the effectiveness of the methodologies employed in this research. Moreover, experimental assessments indicate that optimal efficiency is achieved at equilibrium after 90 minutes for activated carbon derived from date nuts. This computational methodology streamlines the effective handling of empirical data to protect the environment from contaminants such as Cu2+ cations in a manner that is both uncomplicated and time-efficient.

On the measurement of the aerodynamic features of composite structures under subsonic airflow using mathematical modeling and machine learning method

This study investigates the aerodynamic features of functionally graded triply periodic minimal surface (FG-TPMS) structures under subsonic airflow using a combination of mathematical modeling and machine learning methods. The modified supersonic piston theory of Krumhaar is used to quantify the aerodynamic stiffness and damping matrices. Using characteristics and six distinct patterns of volume distribution of FG-TPMS materials in terms of their mechanical qualities, Hamilton’s principle, and parabolic shear deformation theory are used to extract the governing equations of the presented composite structure. After that, the differential quadrature method at the discrete places and Lagrange interpolated polynomials and Kronecker product are used to solve the governing equations in the numerical domain. This study highlights the potential of integrating advanced computational techniques with machine learning to address complex engineering problems. The findings provide valuable insights into the aerodynamic optimization of sandwich structures, paving the way for their more efficient and effective design in aerospace engineering. As an important outcome for related industries, the displacement field along with the Z direction increases by increasing the angle of airflow by approximately 9 % while this value for the X, and Y directions are 7 %, and 6 %, respectively. The proposed methodology offers a powerful tool for engineers and researchers seeking to optimize the performance of advanced composite materials under subsonic airflow conditions.

HIGH-FREQUENCY METHODS FOR COMPLEX AIRBORNE RADAR OBJECTS SCATTERING CHARACTERISTICS CALCULATING

The current state of radar to perform detection and recognition tasks development requires knowledge of a priori information about the secondary radiation of radar objects characteristics. Obtaining this information concerning the target is possible by means of physical or mathematical modelling. Information concerning radar objects obtained by conducting field and physical experiments is associated with significant material, organizational and time costs. Therefore, the method of mathematical modelling can be considered as the most affordable way to obtain information on scattering characteristics. This paper evaluates modern high-frequency methods for the scattering characteristics (secondary radiation) calculating on complex airborne radar objects by mathematical modelling. The calculation of the objects scattering characteristics with surface breaks is carried out by preliminary dividing the surface into a smooth part and edge areas of the surface. The corresponding mathematical relations obtained can be used to estimate the secondary radiation of a complex airborne radar object. The article defines the possibilities of modern high-frequency methods for calculating the scattering characteristics of complex airborne radar objects using mathematical modelling, namely: calculation of scattering characteristics by a smooth surface of a complex airborne radar object; calculation of the scattering characteristics by the edge local surface areas with a radio-absorbing coating of a complex airborne radar object. The scattering characteristics of objects with surface breaks are calculated by first dividing the surface into a smooth part and edge areas. To calculate the scattered field, Kirchhoff-type integral representations are used. Thus, the integration surface covering the scattered in these integral representations is chosen to coincide with the object's surface everywhere except for some edge area. The corresponding mathematical relations for scattering characteristics calculating on smooth and edge localized surface areas of a complex airborne radar object are obtained. The presented calculation methods application can contribute to obtaining a priori information (as required by the current state of radar development) concerning the scattering characteristics of complex airborne radar objects, taking into account such complicating factors as the heterogeneity of the boundary surface, the presence of radio-absorbing coatings, and taking into account their complex effect.

Formulation of nanoemulsion parijoto fruit extract (Medinilla Speciosa) with variation of tweens stabilizers.

Nanotechnology has substantial potential for development due to its ability to modify surface characteristics and particle size, facilitating enhanced absorption of functional food compounds and controlled release of active substances to mitigate adverse effects. Nanoemulsion, a stable colloidal system formed by blending oil, emulsifier, and water, was identified as nanotechnology with promising applications. However, investigations into the impact of surfactants on characteristic nanoemulsions need to be more varied. This research gap necessitated further exploration in the advancement of nanotechnology-based foods. The parijoto fruit (Medinilla speciosa), an indigenous plant species in Indonesia, has yet to undergo extensive scrutiny for its potential use as a functional and nutraceutical food. Anthocyanins, a principal compound in the parijoto fruit, had exhibited efficacy in reducing the risk of cardiovascular disease diabetes, demonstrating anti-inflammatory and antioxidant properties. This study aimed to investigate the characteristics of nanoemulsion formulations derived from parijoto fruit extract and to evaluate an optimum condition with various tween surfactants. The findings from this investigation could furnish valuable insights for the further advancement of anthocyanin nanoemulsions from parijoto fruit extract. The results comprised the characterization of nanoemulsion particle size, polydispersity index, ζ-potential, conductivity, pH, and viscosity. Through mathematical modeling and statistical methods, RSM optimizes nanoemulsion by examining the relationships and interactions between independent and response variables. Furthermore, the characterization of nanoemulsion encompassed ζ-potential, polydispersity, particle size, conductivity, pH, and viscosity. Elevated surfactant concentrations resulted in diminished particle sizes and more uniform size distribution, albeit reaching a plateau where surfactant aggregation and micelle formation ensued. Increased concentrations of surfactant type, concentration, and parijoto extract impacted the physical characteristics of nanoparticle size and polydispersity. The optimal process conditions for nanoemulsion consisting of the type of Tween used are Tween 80, Tween concentration of 12%, and parijoto fruit extract concentration of 7.5%, yielding a desirability value of 0.74, categorizing it as moderate.

Multi-criteria Model for Production Plan Management of a Machine-building Enterprise

The concept of developing an intelligent system to manage the planning of a manufacturing enterprise, and a description of the functionality and modules of the information system are given. In general, operational planning is a complex task of optimizing the construction of a production plan, which includes several criteria and faces various limitations. Multi-criteria is associated with the need for order fulfillment priority in accordance with the law, and the non-linearity of the task is due to technological limitations of production. One of the criteria is to maximize the fulfillment of contractual obligations to supply products to customers. Another criterion is to maximize profits from the sale of the entire range of manufactured products. The limitations in this task are the storage capacity, availability of raw materials and components, the time of operations, the workload of equipment and the priority of orders. Two approaches to solve the optimization problem of managing the production plan are considered, and block diagrams of the implementation of the proposed algorithms are provided. In the first approach, the initial problem is reduced to a combination of linear programming problems, for which the simplex method or the Gomori method are used in practice. A more effective approach to solving this extreme problem is the use of a genetic algorithm and its modifications. The scientific novelty of the conducted research lies in the systematic application of mathematical and computer modeling methods to build an optimal operational production plan. The experience of practical implementation of software systems confirms that intelligent production plan management systems are able to increase the efficiency of enterprise business proce sses, allowing organizations to plan production and allocate resources in market conditions optimally.

The effects of various factors on the efficacy of lithotripsy treatment of urolithiasis

Introduction. Currently, single- and multifactorial criteria are employed to evaluate the quality of urolithiasis treatment utilizing lithotripsy. Among the most utilized single factors that influence the efficacy of urolithiasis therapy are the stone-free rate (SFR), the duration of lithotripsy, the level of intra- and post-operative complications, and hospital stay following lithotripsy. A more promising approach is the integrated indicator of the efficacy of urolithiasis management using the lithotripter, which considers all the aforementioned factors. It is an urgent task to determine the extent to which alterations in individual variables impact the value of an integrated assessment of the efficacy of laser lithotripsy-based urolithiasis intervention.Objective. To study the dependence of the integral efficiency indicator on the magnitude of influencing factors in the treatment of urolithiasis using transurethral thulium lithotripsy.Materials & methods. We used the method of mathematical modeling of the integral criterion for urolithiasis treatment efficacy using the Scilab v.6.02 software package to determine the extent to which individual factors influence the overall effectiveness of laser thulium lithotripsy.Results. Graphical dependences of the index of urolithiasis treatment efficacy for lithotripsy on the complication rate (at different values of surgery time and dependence of urolithiasis treatment efficacy on SFR at different values of complication rate, surgery time and hospital stay) were obtained. A software system for determining the integral index of urolithiasis treatment efficiency for lithotripsy was developed.Conclusion. The resulting dependencies of the index of urolithiasis treatment efficacy for lithotripsy can be used to evaluate the impact of the complication grade and the SFR on the value of the efficacy index and to devise measures to enhance it. The software developed for the calculation of this index allows to obtain the required value at different input influencing parameters.

Wind Power Station Efficiency Increase Methods Based on Wind Turbine Condition Process Mathematical Modelling when Distributing Electric Power Between the Consumers in Arctic and Far North Regions

The relevance of wind power plant efficient control method based on wind turbine condition process mathematical modeling is proved for electric power distribution between consumers, intended to minimize decision-making time on technological process redistribution of electric power production for another consumer by means of actual information on equipment failure time (wind turbine, electric power stocking system), that provides optimum power production and consumption planning in northern regions. The review of the basic mathematical modeling methods of electric power redistribution between consumers that showed there are certain problem statements with insufficient descriptions of mathematical models or the absence of ready and effective methods to solve them, in particular, wind turbine condition process mathematical modeling for electric power distribution to consumers in northern regions. As a result of the analysis of wind power plant efficient control method on the basis of wind turbine condition process mathematical modeling to distribute electric power to consumers in northern regions game theory and pulse system functioning mathematical methods application based on difference equations is expedient. The decision-making strategies stipulated by 'nature' (working capacity or wind turbine failure), the scheduler (repair or wind turbine redistribution) and a condition of phase co-ordinate (repair, idle, redistribution or operation wind turbine modes) are defined. On the basis of the accepted strategy and use of step function Heaviside F(t) for fixing of technological process time, the description of the wind turbine condition equation was made providing operative failure time information access on because due to idle time, redistribution or repair that provides optimum electric power production planning for a consumer.

Dynamical analysis of the pest control model with multiple delays and impulsive effects

In recent years, the suppression of disease population in pest control has gained popularity and remains a pressing issue in agricultural production. Additionally, the mathematical modeling method is often exploited to study the dynamics of different infectious diseases. A new pest control model with multiple delays and impulsive effects is developed and investigated. Firstly, the global attractivity of infection-free periodic solution of the system is proved by applying the theory of impulsive differential equation and comparative theorem. Secondly, the persistence of the infection-free periodic solution of the proposed model is also proved. Finally, the theoretical analysis results are validated by numerical simulations and some suggestions on how to better control the pests are presented.