The paper considers the problem of the approach of two controlled systems describing the dynamics of mathematical pendulums, in which one of the objects seeks to achieve thе meeting, and the other to avoid it. In order to apply the first direct method of L.S. Pontryagin, to solve the problem, a modification of this method was required, based on the application of the time dilation principle. The reason is that the Pontryagin condition, which is the basis of the first direct method and, in fact, provides the possibility of constructing the control at each instant of time according to the current control of the evader, is not satisfied for the problem at hand. This condition reflects the advantage of the pursuer over the evading object in control resources, expressed through the parameters of the systems. A modification of the Pontryagin condition is used, which includes the so-called time dilation function, which plays a decisive role in the construction of the control of the pursuer on the basis of the evaderʼs control in the past, as it were, on the basis of delayed information. For the problem under study, an appropriate function of time dilation is introduced and conditions are derived that ensure the possibility of meeting of the objects in a prescribed finite time. Also, formulas are given that describe the way of constructing the pursuer control on the basis of the adversary control in the past. Using software, a visual illustration of the process of convergence of the objects on the plane, provided the evader is moving in a stable orbit, is created. The algorithm for constructing the current control of the pursuer that leads to the meeting is described.
The problem of increasing the accuracy of determining the orientation of a spacecraft (SC) using a system of star trackers (ST) is considered. Methods are proposed that make it possible to use a joint field of view and refine the relative position of ST to improve the accuracy of orientation determination. The use of several star trackers leads to an increase in the angle between the directions to the stars into the joint field of view, which makes it possible to reduce the condition number of the matrices used in calculating the orientation parameters. The paper develops a combinatorial method for interval estimation of the SC orientation with an arbitrary number of star trackers. To calculate the ST orientation, a linear problem of interval estimation of the orthogonal orientation matrix for a sufficiently large number of stars is solved. The orientation quaternion is determined under the condition that the corresponding orientation matrix belongs to the obtained interval estimates. The case is considered when the a priori estimate of the mutual binding of star trackers can have an error comparable to or greater than the error in measuring the angular coordinates of stars. With inaccurately specified matrices of the mutual orientation of the star trackers, the errors in the mutual orientations of the STs are added to the errors of measuring the directions to the stars, which leads to an expansion of the uncertainty intervals of the right-hand sides of the system of linear algebraic equations used to determine the orientation parameters. A method is proposed for solving the problem of refining the mutual reference of the internal coordinate systems of a pair of ST as an independent task, after which the main problem of increasing the accuracy of spacecraft orientation is solved. The developed method and algorithms for solving such a complex problem are based on interval estimates of orthogonal orientation matrices. For additional narrowing of the intervals, the property of orthogonality of orientation matrices is used. The numerical simulation carried out made it possible to evaluate the advantages and disadvantages of each of the proposed methods.
Today there is a lot of satellite data and products based on it in the public domain. By integrating them with heterogeneous socio-economic information and soil maps, model biophysical data using modern machine learning methods and modern approaches to geospatial data processing, it becomes possible to create maps of land degradation. Considering that classification maps, productivity maps and deforestation maps are the main intellectual components to create a degradation map, it is these products that affect the overall reliability of the results. For their validation, the necessary quality metrics are determined in the work, and the corresponding calculations are made. To evaluate the land cover map, independent test data were used to build a confusion matrix, and the obtained areas of the main crops were compared with statistical data. Agricultural land productivity was estimated using time series land cover classification maps and Crop Growth Modeling System (CGMS) biophysical plant development, as well as biophysical plant growth parameters using satellite data and biophysical plant development models. The LAI Map Accuracy Assessment (based on CGMS) is based on the comparison of Leaf Area Index (LAI) values modeled using the CGMS software framework with LAI ground measurement data collected through ground surveys. Numerous experiments were carried out to assess the quality of models and the results of deforestation maps on an independent test sample, which was not used at the neural network training stage. Degradation maps for several years were also analyzed and their validation was carried out with respect to productivity, in particular for the region that has undergone significant changes for the territory of Ukraine.
The paper investigates the problems of creating a multimedia simulator with a laser emitter for training the correct use of various weapons in order to acquire the skills of targeted high-speed shooting. Specialized Software is designed to train novice shooters and improve the level of fire training in learning the techniques and rules of small arms shooting. The software component consists of separate software modules that allow the user to configure the interactive shooting range, create and run shooting exercises. Hitting the target is determined by the coincidence of the central pixel of the laser response (spot) on the projection image with one of the target pixels. Note that the laser emitter is attached to a real weapon and when you pull the trigger, a spot appears on the screen as a result of the shot. Along with the use of real weapons, computer graphics tools are used to create appropriate virtual environments and simulate a variety of situations in it, as close as possible to real conditions. Hardware and algorithmic shooting errors have been studied and methods for their reduction have been developed. Hardware depends on the parameters of the laser emitter, the size and characteristics of the projection screen, resolution and characteristics of the receiving camera-sensor. Algorithmic depends on the selected algorithm and frame processing methods. The hardware and algorithmic errors of shooting have been investigated and methods have been developed to reduce them. The analysis of the spots from the laser emitter on the projection image and the search for the centroid of the spot are carried out. An algorithm for determining the centroid of a spot through two-stage binarization of the image has been developed and tested, the thresholds of binarization that are optimal for solving the problem have been determined. The test results showed that the obtained accuracy is within the hardware component of the error, and the speed in decision-making is performed in real time.
In various subject areas, the problem of such a distribution of the resources of a controlled system between individual elements (objects) is relevant, which ensures the most efficient functioning of the system in given circumstances. The problem of distribution of the given global resource is considered at restrictions from below, applied on partial resources. It is shown, that the problem consists in construction of adequate criterion function for optimization of process of distribution of resources in conditions of their limitation. The objective function is a scalar convolution of the partial resource vector. Requirements for the objective function: it must penalize partial resources for dangerously approaching its limits and be differentiable in its arguments. In the problem under consideration, partial resources have a dual nature. On the one hand, they can be considered as independent variables, arguments for the optimization of the objective function. On the other hand, it is logical for each of the objects to strive to maximize its partial resource, to go as far as possible from a dangerous limitation in order to increase the efficiency of its functioning. From this point of view, resources can be considered as particular criteria for the quality of the functioning of the corresponding objects. These criteria are subject to maximization, they are limited from below, non-negative and contradictory (an increase in one resource is possible only at the expense of a decrease in others). For the decision of a considered problem the approach of multicriteria optimization with use of the nonlinear trade-off scheme is undertaken. The proposed approach is recommended for a compromise-optimal allocation of resources in a wide range of practical problems. The illustrating example is given.
The three-dimensional problem of elastic membrane dynamics of arbitrary boundary outline with a given superficially distributed external force effect on it, is solved. The three-dimensional field of elastic dynamic displacements of membrane points is described by a differential model, which is a degenerate case of the previously constructed equations of the spatial theory of elasticity concerning thick elastic plates. It is assumed that the latter are supplemented with the information on the initial-boundary condition of the membrane, which in the general case is not of a force nature, and its amount is not sufficient for a mathematically correct formulation of the initial-boundary value problem. The solution of these incompletely defined initial-boundary problems of membrane dynamics became possible after root-mean square mathematical modeling of existing spatial-dynamic observations for the initial condition and current dynamics of its outline by a system of discretely and continuously defined modeling functions. The field of elastic-dynamic displacements of membraneʼ points constructed in the work, being an accurate solution of its differential mathematical model, with the available information on the initial-boundary condition of the latter, is consistent with the root-mean square criterion. Estimations of the accuracy of such modeling are made and conditions for its uniqueness are formulated in the paper. Cases of purely transverse and purely planar oscillations of the membrane are considered. The numerical realization of the obtained considered problemsʼ solution is conducted even with a minimum number of observations for the membraneʼs condition confirms the simplicity and correctness of the approach to these mathematically complex problemsʼ research of elastic-dynamics of thick elastic plates.
The paper considers the problem of modeling the dynamics of computer viruses spreading using a model based on the mathematical theory of biological epidemics. The urgency of the considered problem arises from the need to build effective anti-virus protection systems for computer networks based on the results of mathematical modeling of the spread of malicious software. We consider the SIES-model (Gan C., Yang X., Zhu Q.), that studies spread dynamics of computer viruses separating the influence of the action of computers accessible and unavailable on the Internet. In order to take into account non-local effects in this model, in particular memory effects, its modification on the ideas of the theory of fractional-order integro-differentiation is proposed. The technique of obtaining a numerical-analytical solution of the problem of modeling of computer viruses spread dynamics on the base of the fractional-differential counterpart of the SIES-model is presented. Closed forms solutions of the problems for the number of vulnerable and external computers are obtained, and a finite-difference scheme of the fractional Adams method for the problem of determining the number of infected computers is constructed. The results of computational experiments based on the developed technique of numerical-analytical solution show that there is a subdiffusion evolution of the system to the steady state. At the same time, for the number of external computers, a fast short-term growth is observed at the initial stages of process development with subsequent smooth and slow decrease towards the steady state. For medium and large values of the time variable, the evolution of the number of infected computers to the steady state occurs in an ultra-slow mode. Thus, the proposed technique makes it possible to study the families of dynamic reactions in the process of computer viruses spreading, including fast transient processes and ultra-slow evolution of systems with memory.
Researches of the subject area of lossless information compression and with data loss are carried out and data compression algorithms with minimal redundancy are considered: Shannon-Fano coding, Huffman coding and compression using a dictionary: Lempel-Ziv coding. In the course of the work, the theoretical foundations of data compression were used, studies of various methods of data compression were carried out, the best methods of archiving with encryption and storage of various kinds of data were identified. The method of archiving data in the work is used for the purpose of safe and rational placement of information on external media and its protection from deliberate or accidental destruction or loss. In the Embarcadero RAD Studio XE8 integrated development environment, a software package for an archiver with code protection of information has been developed. The archiverʼs mechanism of operation is based on the creation and processing of streaming data. The core of the archiver is the function of compressing and decompressing files using the Lempel-Ziv method. As a method and means of protecting information in the archive, poly-alphabetic substitution (Viziner cipher) was used. The results of the work, in particular, the developed software can be practically used for archival storage of protected information; the mechanism of data archiving and encryption can be used in information transmission systems in order to reduce network traffic and ensure data security. The resulting encryption and archiving software was used in the module of the software package «Diplomas SNU v.2.6.1», which was developed at the Volodymyr Dal East Ukrainian National University. This complex is designed to create a unified register of diplomas at the university, automate the creation of files-diplomas of higher education in the multifunctional graphics editor Adobe Photoshop. The controller exports all data for analysis and formation of diplomas from the parameters of the corresponding XML files downloaded from the unified state education database in compressed zip archives. The developed module performs the process of unzipping and receiving XML-files with parameters for the further work of the complex «Diplomas SNU v.2.6.1».
The article deals with the topical issue of quantitative assessment of technological singularity. The authors made an analysis of artificial intelligence tools and approaches affecting the development of superintelligence, which allowed for the first time to develop a general multifactor model of technological singularity and present it in the space of direct and indirect indicators of development. The developed approach makes it possible to move from expert judgments on the issue of technological singularity in the form of extrapolated complexity curves of various systems or qualitative description of possible scenarios of technological development to quantitative assessment of the state of technological singularity. The links between the relevant functional areas of human intelligence and modern expert systems are formalized, a structural-functional model of knowledge acquisition is developed. A conclusion is made about the real limits of the processes of modern "intelligent" systems at the level of artificial thinking and logical cognition, which corresponds to a weak artificial intelligence. The state and ways of hardware development were analyzed, which allowed making a conclusion about the complex use of different hardware architectures and information processing principles: supercomputer, neurosynaptic and quantum computers to implement the concept of technological singularity. Formalized in the form of a structural model the areas of research most influential in the development of artificial intelligence, and their relationship to existing approaches and methods of processing big data. For the first time proposed the classification of indicators of development of artificial intelligence within two classes: direct and indirect, grouped into three groups: the intensity of research and public activity; the level of applied (technological) solutions; practical implementation, most affecting the development of general artificial intelligence. The correlation between the formalized groups of indicators was revealed, which confirms the correctness of the hypothesis about the cause-effect relationship between the groups: theoretical research → applied solutions → practical implementation and their mutual influence.
The main attention is paid to the estimation of the optimal number of clusters for the system given by the node adjacency matrix Based on the assumptions about the similarity of connections in the cluster, the conclusion was drawn about optimal number of clusters for different applications. Poisson's network of connections is modeled and the optimal number of clusters is found. The simulation results indicate high accuracy in determining the optimal number of clusters. In the basic theorem, it is important to assume the existence of a moment above the second for each element of the matrix However, taking into account normalization, this condition can be reduced to the existence of a mathematical expectation of the matrix This weakening of the convergence conditions makes it possible to use a proven statement for a wider class of applied problems, where the presence of a finite variance is not required. Note that the emissions are valid eigenvalues for the normalized matrix, which allows you to localize quickly emissions with complexity where — the number of system nodes. Thus, we managed to weaken two important assumptions about the distribution of elements of a random matrix, namely the assumption about the equality of 0 mathematical expectations of the elements of the matrix and the independence of the elements of the matrix. In addition, the independence of the elements can be replaced by weak independence, which maintains convergence to the mean value in the law of large numbers.
Over the past few decades, the theory of pseudodifferential operators (PDO) and equations with such operators (PDE) has been intensively developed. The authors of a new direction in the theory of PDE, which they called parabolic PDE with non-smooth homogeneous symbols (PPDE), are Yaroslav Drin and Samuil Eidelman. In the early 1970s, they constructed an example of the Cauchy problem for a modified heat equation containing, instead of the Laplace operator, PDO, which is its square root. Such a PDO has a homogeneous symbol |σ|, which is not smooth at the origin. The fundamental solution of the Cauchy problem (FSCP) for such an equation is an exact power function. For the heat equation, FSCP is an exact exponential function. The Laplace operator can be interpreted as a PDO with a smooth homogeneous symbol |σ|^2, σ ∈ Rn. A generalization of the heat equation is PPDE containing PDO with homogeneous non-smooth symbols. They have an important application in the theory of random processes, in particular, in the construction of discontinuous Markov processes with generators of integro-differential operators, which are related to PDO; in the modern theory of fractals, which has recently been rapidly developing. If the PDO symbol does not depend on spatial coordinates, then the Cauchy problem for PPDE is correctly solvable in the space of distribution-type generalized functions. In this case, the solution is written as a convolution of the FSCP with an initial generalized function. These results belong to a number of domestic and foreign mathematicians, in particular S. Eidelman and Y. Drin (who were the first to define PPDO with non-smooth symbols and began the study of the Cauchy problem for the corresponding PPDE), M. Fedoruk, A. Kochubey, V. Gorodetsky, V . Litovchenko and others. For certain new classes of PPDE, the correct solvability of the Cauchy problem in the space of Hölder functions has been proved, classical FSCP have been constructed, and exact estimates of their power-law derivatives have been obtained [1–4]. Of fundamental importance is the interpretation of PDO proposed by A. Kochubey in terms of hypersingular integrals (HSI). At the same time, the HSI symbol is constructed from the known PDO symbol and vice versa [6]. The theory of HSI, which significantly extend the class of PDO, was developed by S. Samko [7]. We extends this concept to matrix HSI [5]. Generalizations of the Cauchy problem are non-local multipoint problems with respect to the time variable and the problem with argument deviation. Here we prove the solvability of a nonlocal problem using the method of steps. We consider an evolutionary nonlinear equation with a regularized fractal fractional derivative α ∈ (0, 1] with respect to the time variable and a general elliptic operator with variable coefficients with respect to the second-order spatial variable. Such equations describe fractal properties in real processes characterized by turbulence, in hydrology, ecology, geophysics, environment pollution, economics and finance.
For early detection and timely correction of imbalances in the body that can lead to the development of various diseases, personalized devices are needed with which one can control the current state of the body at home. The purpose of the article is to develop a universal approach to the construction of such tools and, using examples of solving urgent problems, to demonstrate its effectiveness. A distinctive feature of the proposed approach is that the user at home has the ability to form a training sample of observations of his physiological indicators, according to which two integral characteristics are automatically calculated: the reference result, which is closest to all other observations, and the value, characterizing the average deviation of the results. Personalized diagnostic rules are proposed that ensure an increase in the reliability of decisions about the current functional state of the user and an assessment of the risk of a possible development of pathology. The proposed rules form the basis of original preventive medicine for home use, including the intelligent PHASEGRAPH® electrocardiograph for diagnosing myocardial ischemia at early stages, AI-RHYTHMOGRAPH software applications for determining heart rate variability parameters and AI-ARTERIOGRAPH for integral assessment of properties blood vessels, an intelligent blood pressure monitor that measures the long-term variability in blood pressure between doctor visits, and an intelligent stethoscope for detecting respiratory distress at home. Further development of the proposed approach will make it possible to create personalized means of assessing visual acuity and hearing acuity at home, control of the vestibular apparatus, essential tremor and other means.
Due to the widespread use of sensors in data collection and processing, one of the key criteria is the amount of information accumulated and energy efficiency. While monitoring the territory, the movement of research objects is common. As a result there is a change in the probability of their detection in the segment of the territory. Also, segments may be of varying importance. Taking these factors into account will significantly increase the amount of information accumulated. The article presents a method of constructing the optimal trajectory of sensors motion taking into account the importance of territory segments and the probability of detection of objects. The method is based on the representation of distribution of the probability of detection of objects and the importance of territory segments in the form of layers and their integration into a layer of the probable value of detected objects. Seven classes of the probable value of detected objects with corresponding numerical and graphical equivalents are considered. As optimal trajectory of sensors motion the trajectory which provides minimum energy expenditure is meant. Energy efficiency is achieved by constructing a trajectory of minimum length as a solution to the salesman’s problem. The set of points at which the trajectory is built is formed on the basis of the layer of the probable value of the detected objects after the procedure of replacing the nodes. A separate node replacement class, or superposition of node replacement classes, is proposed for each class of probable value of detected objects. Replacement of five, three and two nodes is described. A genetic algorithm with modification of crossing and selection rules was used to find a solution to this problem. A set of trajectories is constructed using the proposed algorithm. The analysis of the obtained results confirmed the efficiency of the developed method and allowed to increase the energy efficiency when covering a given area by 76 %.
Various mathematical models are created for exploring complex self-organizing systems. In geosystems, the deterministic nature of processes is due to their stochastic properties. In such systems, regular deterministic processes are formed by numerous random interelement interactions that occur at the micro level. In many cases, it is not possible to define correctly the deterministic law of evolution of the observable system or its part because of the large number of unpredictable and unknown factors that influence it. However, at the micro level, statistical distributions of system elements are available for observation, which allows to predict its behavior and evaluate the factors influencing the system. The most universal methods for modeling systems with stochastic properties are based on the fundamental concepts of statistical mechanics — the Gibbs-Shannon and Renyi information entropies. The article studies the entropy methods for calculating quantitative estimations of the states of spatially distributed geosystems and their divergences in the process of self-organization: alpha-divergence, Kullback divergence, variability of the spectrum of Renyi dimensions. The features of the above systems with multifractal structures according to hyperspectral measurements are observed. The examples illustrate the use of entropy models in numerical experiments with real data obtained from a natural gas field. Verification of the entropy methods for determining the boundaries of hydrocarbon deposits based on the hyperspectral data of emission of a homogeneous vegetation cover was carried out.
The laser irradiation of metallic surfaces by intense heat sources is used for the generation of short probing pulses, which propagate into thin specimens and enable one to estimate their structure and mechanical properties within the framework of the classical acoustic approach. High thermal stresses and residual strains occur during the short-term irradiation of the surface of a construction by an energy source of high density. In the present work, we solve the axially symmetric problem of a half-space under thermomechanical loading. We take into account the influence of volume and inelastic characteristics of separate phases on the residual stress-strain state of the half-space. The statement of the problem includes: Cauchy relations, equations of motion, heat conduction equation, initial conditions, thermal and mechanical boundary conditions. The thermomechanical behavior of an isotropic material is described by the Bodner-Partom unified model of flow. The problem is solved with using the finite element technique. The numerical realization of our problem is performed with the help of step-by-step time integration. The equations of motion are integrated by the Newmark method. The residual stress-strain state is described using the method of numerical solution of the axisymmetric dynamic problem for a half-space under thermomechanical loading and the flow model. We established that microstructural transformations, which are taken into account due to the thermophase volume strain and dependence of inelastic characteristics of the material on the phase composition, significantly reduce residual inelastic strain and promote the appearance of compressive stresses. The three-zone region of residual stresses field formation is obtained.
We study a differential game of approach in a delay stochastic system. The evolution of the system is described by Ito`s linear stochastic differential equation in Hilbert space. The considered Hilbert spaces are assumed to be real and separable. The Wiener process takes values in a Hilbert space and has a nuclear symmetric positive covariance operator. The pursuer and evader controls are non-anticipating random processes, taking on values, generally, in different Hilbert spaces. The operator multiplying the system state is the generator of an analytic semigroup. Solutions of the equation are represented with the help of a formula of variation of constants by the initial data and the control block. The delay effect is taken into account by summing shift type operators. To study the differential game, the method of resolving functions is extended to case of delay stochastic systems in Hilbert spaces. The technique of set-valued mappings and their selectors is used. We consider the application of obtained results in abstract Hilbert spaces to systems described by stochastic partial differential equations with time delay. By taking into account a random external influence and time delay, we study the heat propagation process with controlled distributed heat source and leak.
We consider one method of solving the problem of mathematical safe on certain graphs called parametric. Its gist consist in denoting some variables, corresponding to graph vertices, by certain parameters. Other unknown variables are expressed through these parameters. Then unknown variables chosen in special way are compared and the mentioned parameters are found by solving additional system of equations for these parameters. Dimension of this system is equal to the number of parameters. Solution to the problem i.e. all unknown variables of the original system, are found by solving additional system of equations. In the paper this method is described on specially chosen examples. The method is demonstrated by solving the mathematical safe problem on the graphs of «chain», «ladder» and «window» types that showed its efficiency. Besides special attention is paid to special cases when solution does not exist. This occurs in the cases when the weighed sum of system equations is not divisable without remainder to its modulo. In such cases, to find solution the initial state of the vector b is corrected in such a way that the weighted sum of equations satisfies the above mentioned condition. Then solution of the problem is performed according to the general method scheme.
Метод ADMM (alternating direction methods of multipliers) широко используется для решения многих оптимизационных задач с помощью параллельных вычислений. Этот метод особенно важен при решении задач, возникающих в машинном обучении, математической статистике, распознавании образов, восстановлении сигналов, обработке данных значительного объема. ADMM позволяет решать оптимизационные задачи, целевая функция которых представляет собой сумму гладкой и негладкой функций, что характерно для задач со штрафной функцией. Целью этой статьи является разработка улучшенной версии ADMM с лучшей скоростью сходимости, чем существующие методы. В статье описаны существующие подходы для улучшения эффективности ADMM-метода, приведены основные работы по данной тематике и предложен новый метод, базирующийся на комбинации двух уже существующих подходов - разбиение начальной оптимизационной задачи на N подзадач и применение многоблочного подхода для разрешение и вычисление ускорения Нестерова на каждой итерации. Приведены теоретическое обоснование сходимости данного метода и установлены условия сходимости. Реализован предлагаемый алгоритм языка программирования Python и применен для решения задачи обмена с генерируемыми случайным образом данными, задачи поиска базиса и задачи LASSO с ограничениями. Приведены результаты сравнения эффективности многоблочного ADMM с ускорением Нестерова и существующих многоблочного и стандартного двухблочного ADMM. Многоблочный ADMM с ускорением Нестерова показал лучшую вычислительную эффективность, чем уже существующие методы. Еще одним преимуществом предлагаемого метода является его удобство для проведения параллельных вычислений с применением современных многопроцессорных систем. В связи с большими объемами данных, обработка которых требует значительного времени при решении оптимизационных задач, предложенный метод имеет важное практическое значение, поскольку он значительно превышает по скорости известные аналоги. Использование предложенного метода позволит решить практически важные задачи большого объема, применив параллельные вычисления.
Разработаны основы математического моделирования и идентификации параметров неоднородных анормальных неврологических движений (АНР) в многокомпонентных нейробиосистемах с обратными когнитивными связями. На основе развитых авторами методов интегральных превращений и спектрального анализа для неоднородных сред предложен новый подход к построению гибридных моделей распространения волнового сигнала, описывающего нежелательные дрожания конечности руки пациента (Т-объекта) в результате самопроизвольного сокращения скелетных мышц. за счет когнитивных воздействий отдельной группы нейронных узлов коры головного мозга (КГМ). Разработана гибридная модель нейробиосистемы, описывающая состояние и поведение Т-объектов, а именно посегментное описание 3D-элементов траекторий АНР Т-объекта с учетом матрицы когнитивных воздействий групп нейроузлов КГМ. На основе гибридных интегральных преобразований Фурье получено высокоскоростное аналитическое векторное решение модели, описывающей элементы траекторий на каждом АНР-сегменте. Предложена новая методика вычисления гибридной спектральной функции, спектральных значений и матрицы когнитивных воздействий нейроузлов КГМ, определяющих гибридное интегральное преобразование построения решения. Сформулированы и решены новые неклассические задачи многопараметрической идентификации нейросистем с обратной связью в неоднородных средах на основе минимизации функционала-невязки между траекториями наблюдения и их модельными аналогами. Построены высокопроизводительные алгоритмы идентификации амплитудно-частотных характеристик систем обратной связи для компонентной оценки влияния когнитивных обратных связей, позволяющих распараллелировать вычисления для многоядерных компьютеров. Выполнено компьютерное моделирование и идентификацию АНР-траекторий нейросистем обратной связи.
Работа посвящена проблеме создания новых методов для комплексного моделирования и управления риском, которые позволят исследовать синергетические взаимодействия между источниками рисков различного происхождения в условиях неопределенности. Предложен подход к исследованию взаимосвязи продовольственных, водных и энергетических ресурсов с помощью трехсекторальной модели Лоренца, которая объединяет в единой структуре однотипным образом описанные сектора экономики, каждый из которых рассматривается в сроках уровня производительности, количества рабочих мест. и уровня структурных нарушений В результате математического моделирования определены условия возникновения детерминированного хаоса в минимальной модели экономического развития и выявлены возможные причины возрастающей уязвимости глобальной экономики к малым изменениям параметров управления. Рассмотрена задача определения эффективных управлений с целью минимизации суммарных структурных нарушений за выбранный интервал времени. В результате модельных экспериментов обнаружены траектории изменения параметров управления, позволяющие уменьшить число структурных нарушений. Это достигается за счет изменений соотношения уровней пропозиции и спроса продукции, спроса и предложения на создание рабочих мест. Рассмотрено влияние случайных возмущений на стохастическую деформацию детерминированных аттракторов модели Лоренца. Показано, что при случайных возбуждениях траектории стохастической системы покидают детерминированный аттрактор и образуют вокруг него некоторый пучок с соответствующим вероятностным распределением. Рассмотрена возможность дальнейшего усложнения модели за счет учета других секторов экономики с помощью модели Лоренца в комплексной форме. Задача исследования n секторов экономик в этом случае сводится к рассмотрению поведения ансамбля n связанных осцилляторов, генерирующих колебания с частотами ωn соответственно. Коллективная синхронизация данных осцилляторов может быть исследована с помощью модели Курамото. Задача управления социально-экономическим развитием в условиях возникновения хаотических режимов сводится для комплексной модели к управлению частотой поля с ненулевым средним, генерируемым связанными осцилляторами.
