scholarly journals MODELING THE DEVELOPMENT OF EPIDEMIS BASED ON INFORMATION TECHNOLOGIES OF OPTIMIZATION

2021 ◽  
pp. 47-52
Author(s):  
Olena Nikulina ◽  
Valerii Severyn ◽  
Mariia Naduieva ◽  
Anton Bubnov
Keyword(s):  
Information Technology ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Dynamic Systems ◽  
Information Technologies ◽  
Model Parameters ◽  
Infected People ◽  
Systems Of Differential Equations ◽  
Epidemic Development

Mathematical models of the epidemic have been developed and researched to predict the development of the COVID-19 coronavirus epidemic on thebasis of information technology for optimizing complex dynamic systems. Mathematical models of epidemics SIR, SIRS, SEIR, SIS, MSEIR in theform of nonlinear systems of differential equations are considered and the analysis of use of mathematical models for research of development ofepidemic of coronavirus epidemic COVID-19 is carried out. Based on the statistics of the COVID-19 coronavirus epidemic in the Kharkiv region, theinitial values of the parameters of the models of the last wave of the epidemic were calculated. Using these models, the program of the first-degreesystem method from the module of information technology integration methods for solving nonlinear systems of differential equations simulated thedevelopment of the last wave of the epidemic. Simulation shows that the number of healthy people will decrease and the number of infected peoplewill increase. In 12 months, the number of infected people will reach its maximum and then begin to decline. The information technology ofoptimization of dynamic systems is used to identify the parameters of the COVID-19 epidemic models on the basis of statistical data on diseases in theKharkiv region. Using the obtained models, the development of the last wave of the COVID-19 epidemic in Kharkiv region was predicted. Theprocesses of epidemic development according to the SIR-model with weakening immunity are given, with the values of the model parameters obtainedas a result of identification. Approximately 13 months after the outbreak of the epidemic, the number of infected people will reach its maximum andthen begin to decline. In 10 months, the entire population of Kharkiv region will be infected. These results will allow us to predict possible options forthe development of the epidemic of coronavirus COVID-19 in the Kharkiv region for the timely implementation of adequate anti-epidemic measures.

MODELS OF WWER-1000 NUCLEAR REACTOR WITH DIVISION INTO ZONES ON VERTICAL AXIS FOR INFORMATION TECHNOLOGY OF CONTROL

2021 ◽  
Vol 4 ◽  
pp. 105-116
Author(s):  
Valeriy Severyn ◽  
◽  
Elena Nikulina ◽  
◽  
Keyword(s):  
Information Technology ◽  
Differential Equations ◽  
Mathematical Models ◽  
Nuclear Power ◽  
Nuclear Reactor ◽  
Control Object ◽  
Vertical Axis ◽  
State Variables ◽  
Relative State ◽  
Systems Of Differential Equations

Mathematical models of the WWER-1000 nuclear power reactor have been developed with division into zones along the vertical axis in the form of nonlinear systems of differential equations with dimensionless relative state variables. Models in a given number of zones along the vertical axis represent neutron kinetics, gradual heat release, thermal processes in fuel, cladding and coolant, changes in the concentration of iodine, xenon and boron. The parameters of mathematical models have been calculated based on the design and technological parameters of the V-320 series nuclear reactor. A general model of the reactor as a control object with division into zones along the vertical axis, as well as models with control of absorbing rods and boric acid, are obtained. Integration of the obtained systems of differential equations for given initial conditions allows one to obtain changes in all state variables in the reactor zones along the vertical axis. In particular, from the change in power in the zones along the vertical axis, the axial offset is calculated as the relative value of the difference between the powers of the upper and lower halves of the reactor core. The developed reactor models with dimensionless relative state variables use a minimum number of calculations, allow calculating the change in the axial offset, and are included in the information technology for controlling the power units of nuclear power plants to optimize the maneuvering modes of the WWER-1000 V-320 series reactor.

APPLICATION OF INFORMATION TECHNOLOGY FOR MODELING THE CONTROL DYNAMICS OF A NUCLEAR REACTOR ZONING ON THE VERTICAL AXIS

2021 ◽  
Vol 5 ◽  
pp. 45-56
Author(s):  
Valery Severyn ◽  
◽  
Elena Nikulina ◽  
Keyword(s):  
Information Technology ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Control Systems ◽  
Nuclear Reactor ◽  
Initial Conditions ◽  
Control Object ◽  
Vertical Axis ◽  
Integration Methods ◽  
Systems Of Differential Equations

The structure of information technology for modeling control systems, which includes a block of systems models, a module of integration methods and other program elements, is considered. To analyze the dynamics of control of a nuclear reactor, programs of mathematical models of a WWER-1000 nuclear reactor of the V-320 series and its control systems in the form of nonlinear systems of differential equations in the Cauchy form have been developed. For the integration of nonlinear systems of differential equations, an algorithm of the system method of the first degree is presented. A mathematical model of a WWER-1000 reactor as a control object with division into zones along the vertical axis in relative variables of state is considered, the values of the constant parameters of the model and the initial conditions corresponding to the nominal mode are given. Using information technology for ten zones of the reactor, the system integration method was used to simulate the dynamics of control of a nuclear reactor. Graphs of neutron and thermal processes in the reactor core, as well as changes in the axial offset when the reactor load is dumped under the influence of the movement of absorbing rods and an increase in the concentration of boric acid, are plotted. The analysis of dynamic processes of reactor control is carried out. The programs of integration methods and models of the WWER-1000 reactor of the V-320 series are included in the information technology to optimize the maneuvering modes of the reactor.

scholarly journals Grounds for Searching the Best Solution for Controlling the Pressurized Water Reactor in Dynamic Modes when Changing the Controlled Parameters

2021 ◽  
Vol 7 (1) ◽  
pp. 56-61
Author(s):  
Taia Petik ◽  
◽  
Viktoriia Vataman ◽  
Konstantin Beglov ◽  
Anna Lysyuk
Keyword(s):  
Information Technology ◽  
Differential Equations ◽  
Control Systems ◽  
Dynamic Systems ◽  
Quality Criteria ◽  
System Quality ◽  
Complex Dynamic ◽  
Complex Dynamic Systems ◽  
Systems Of Differential Equations ◽  
Analysis And Synthesis

The article focused on the development of information technology for the optimization of control over complex dynamic systems at the stage of their design that should realize possibilities of modeling of linear and nonlinear dynamic systems, the analysis and synthesis of such systems, their optimization on various quality criteria. The purpose of this article is to develop the structure and elements of information technology to optimize the control of complex dynamic systems, including automated control systems. The general structure and functional model of information technology of the analysis and synthesis of control systems includes modeling of dynamic systems in the form of systems of differential equations and transfer functions, integration of systems of differential equations, calculation of system quality criteria, methods for solving various optimization tasks on solutions of optimization problems of dynamic systems is offered.

scholarly journals Cone valued Lyapunov functions and Lipschitz stability of nonlinear systems of differential equations

1996 ◽  
Vol 19 (3) ◽  
pp. 435-440
Author(s):  
Olusola Akinyele
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Lyapunov Functions ◽  
Practical Stability ◽  
Lipschitz Stability ◽  
Comparison Result ◽  
Systems Of Differential Equations ◽  
New Concepts ◽  
Perturbed Systems

We introduce a new comparison result which will be an important tool when we apply cone valued Lyapunov like functions. We also introduce new concepts ofϕ0-uniform Lipschitz stability and(λ,λ,ϕ0)-practical stability and employ our comparison result to carry out stability analysis of nonlinear systems. Our results are also applicable to nonlinear perturbed systems.

scholarly journals DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1998 ◽  
Vol 3 (1) ◽  
pp. 45-56
Author(s):  
T. Cîrulis ◽  
O. Lietuvietis
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Matrix Method ◽  
Iteration Procedure ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Systems Of Differential Equations ◽  
Runge Kutta ◽  
Degenerate Matrix

Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given.

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