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Investigation of the dynamics of singular protected systems

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EN
Abstrakty
EN
The analysis of asymptotic representations of the systems protected from harmful influences is carried out. Various types of general models of the "manmachineenvironment" with protection are considered. Each of them adequately describes some of the practically important qualities of the object, and they all together describe the object in terms of its safe operation. The dynamic properties of complex ergonomic systems, presented in the form of systems of differential equations with a small parameter at the derivative are investigated The methods of reducing the impact on the person of harmful factors are theoretically substantiated. The dynamic protection response speed is considered to be significantly greater than the harmful factor production rate. Numerical solution of the general problem and the analytical solution for autonomous case is obtained for harmful effects. By using asymptotic the system of equations has been solved in closed form not only for autonomous case, but also for parameters smoothly changing in time. The estimates of the cost of protection was obtained for the various cost-functionals and for different functions in the right-hand side of the equation describing the dynamics of protection. To assess the accuracy of model calculations and for graphic representation of the results mathematical package MAXIMA is used.
Twórcy
autor
  • Kharkov National University of Radio Electronics
  • Kharkov National University of Radio Electronics
Bibliografia
  • 1. Alexeev I., Voloshyn O., 2013. Formation of Compensation Mechanism of Regional Enterprises’ Human Resources Regeneration in the Labor Potential Development System. ECONTECHMOD. An International Quarterly Journal. Vol. 2. No. 3, 3-8
  • 2. Saati Т. 1993. Decisions making. Method of hierarchy analysis. M.: Radio& communication, 282. (in Russian).
  • 3. Dzundzjuk B., Naumeyko I., Serdyuk N., 2000. Content model for number of harmful factors of impact on human. Radioelektronika i informatika, №3(12), 127-128. (in Russian).
  • 4. Haken H., 2004. Synergetics: introduction and advanced topics. Springer-Verlag, 201.
  • 5. Vasil'eva A., Butuzov V., 1990 Asymptotic expansions of solutions of singularly perturbed equations.- Moscow: Higher School. 201 (in Russian).
  • 6. Naumeyko I., Al-Refai V., 2013. Concerning issue of critical regimes analysis with dynamic defense systems from harmful influence / Information systems and technologies // Materials 2 Intern. Science and Techn. Conf. - Kharkiv. NTTM. 12. (in Russian).
  • 7. Naumeyko I., 2011. Critical points of dynamic model for harmful factors distributing. Materials of International scientific conference ISTE 2011. Kharkov- Yalta. October 1-6 2011, 60-61 (in Russian).
  • 8. Naumeyko I., Alja'afreh M., 2015. Dynamic balance research of protected systems. ECONTECHMOD. An International Quarterly Journal. vol.4, No 3 – P. 85–90.
  • 9. Inozemtsev G., 2012. Scientific and technical preconditions of electric field application at plants protection. ECONTECHMOD. An International Quarterly Journal. Vol. 1. No. 1, 47-50.
  • 10. Ilyichev V., 2003. Stabilization and adaptation mechanisms in ecology models: Dis. ... Doctors of technology sciences : 05.13.01, 05.13.18 : Rostov-on- Don, 279. RGB OD, 71:04-5/418. (in Russian).
  • 11. Nasritdinov G. and Dalimov R., 2010. Limit cycle, trophic function and the dynamics of intersectoral interaction. Current Research J. of Economic Theory, 2(2), 32–40.
  • 12. Brauer F., Castillo-Chavez C., 2000. Mathematical Models in Population Biology and Epidemiology. Springer-Verlag, 412.
  • 13. Hoppensteadt F., 2006. Predator-prey model. Scholarpedia, 1(10), 1563.
  • 14. Jost C., Devulder G., Vucetich J., Peterson R., Arditi R., 2005. The wolves of Isle Royale display scaleinvariant satiation and density dependent predation on moose. J. Anim. Ecol. 74(5), 809–816.
  • 15. Arditi R., Ginzburg L., 2012. How Species Interact: Altering the Standard View on Trophic Ecology. Oxford University Press. ISBN 9780199913831.
  • 16. Sahal D., 1976. System Complexity: Its Conception and measurement in the Design of Engineering systems. IEEE Trans. Syst. Man. Cybern., SMC 6, 152.
  • 17. Arrowsmith D., Place C., 1986. Ordinary differential equations. A qualitative approach with applications. М.: Mir, 243. (in Russian).
  • 18. Andrianov I., Barantsev R., Manevitch L., 2004. Asymptotic Mathematics and Synergetics. M.: Publishing house "Editorial URSS", 304. (in Russian).
  • 19. Sidorov S., 2009. Mathematical and numerical study of dynamic chaos in dissipative systems of nonlinear differential equations: Thesis ... doctor of Mathematics and Physics science : 05.13.18 ; [Place of defense: Moscow state municipal university].- Moscow, 2009, 283 : il. RGB OD, 71 10-1/73. (in Russian).
  • 20. Amirokov S., 2006. Numerical methods and simulation experiment in research of dynamics and structure of interacting societies: Thesis ... Candidate of Physical and Mathematical Science : 05.13.18.- Stavropol 2006, 187 : il. RGB OD, 61 06-1/929. (in Russian).
  • 21. Ilyina V., Silaiev P., 2004 PK MAXIMA computer algebra system for theoretical physicists. M.: Moscow State University. 113. (in Russian).
  • 22. Koronovskiy A., 2007. Synchronized behavior, complicated dynamics and transmission processes in selfsustained oscillation systems and standard reference models of non-linear theory of oscillations : thesis ... Doctor of Physics and Mathematics science : 01.04.03; [Place of defense: Saratov State University].- Saratov, 2007, 462 : il. RGB OD, 71 07-1/420. (in Russian).
  • 23. Latypov V., 2010. Mathematical models of perturbed motion of a high order of accuracy: thesis ... candidate of Physics and Mathematics science : 05.13.18; [Place of defense: St-Petersburg state university].- St- Petersburg, 2010, 133: il. RGB OD, 61 10-1/736. (in Russian).
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-69a2d34c-df3d-45e8-8096-e1598c9f3349
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