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Mathematical Modeling of Some Physical Phenomena Through Dynamical Systems

  • Olivia Ana Florea
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 179)

Abstract

The differential equations and system of differential equations represent the kernel of the mathematical modeling, offering tools to predict the natural phenomena from science, technics, medicine, biology, etc. In this chapter we will analyze the phase portraits of different dynamical systems linear and non-linear, the lagrangian formalism of a problem encountered in aerodynamics and averaging method for nonlinear differential equation.

References

  1. Belousov, B.P.: Periodicheski deistvuyushchaya reaktsia i ee mekhanism [Periodically acting reaction and its mechanism]. In: Sbornik referatov po radiotsionnoi meditsine [Collection of Abstracts on Radiation Medicine], 1958, pp. 14–147. Moscow, Medgiz (1959)Google Scholar
  2. Bârzu, A., Bourceanu, G., Onel, L.: Nonlinear dynamics. MatrixRom, Bucharest (2003)Google Scholar
  3. Broer, H., Takens, F.: Dynamical Systems and Chaos. Springer, Berlin (2009)Google Scholar
  4. Carstea, C., Enache-David, N., Sangeorzan, L.: Fractal model for simulation and inflation control. In: Bulletin of the Transilvania University of Brasov. Series III: Mathematics, Informatics, Physics, vol. 7(56), issue 2, pp. 161–168 (2014)Google Scholar
  5. Coayla-Teran, E.A., Mohammed, S.-E.A., Ruffino, P.R.C.: Theorems along hyperbolic stationary trajectories. South. Ill. Univ. Carbondale OpenSIUC 2, 1–18 (2007)zbMATHGoogle Scholar
  6. Enache-David, N., Sangeorzan, L.: An application on web path personalization. In: Proceedings of the 27th International Business Information Management Association Conference - Innovation Management and Education Excellence Vision 2020: From Regional Development Sustainability to Global Economic Growth, Milan, Italy, pp. 2843–2848 (2016)Google Scholar
  7. Florea, O., Purcaru, M.: Mathematical modeling and the stability study of some chemical phenomena. Proc. AFASES 1, 525–529 (2012)Google Scholar
  8. Kuznetsov, N.V.: Stability and Oscillations of Dynamical Systems: Theory and Applications. Jyvaskyla Studies of Computing (2008)Google Scholar
  9. Li, J.: Hilbert’s 16th problem and bifurcations of planar polynomial vector fields. Int. J. Bifurc. Chaos 13(1), 47–106 (2003)MathSciNetCrossRefGoogle Scholar
  10. Lotka, A.J.: Undamped oscillations derived from the law of mass action. J. Am. Chem. Soc. 42, 1595–1599 (1920)CrossRefGoogle Scholar
  11. Lungu, N., Chisalita, A.: Dynamical Systems And Chaos. MatrixRom, Bucharest (2007)Google Scholar
  12. Lupu, M., Postelnicu, A., Deaconu, A.: A Study on the flutter stability of dynamic aeroelastic systems. In: Proceedings CDM , pp. 37–46. Brasov (2001)Google Scholar
  13. Obadeanu, V., Neamtu, M.: Systemes dynamiques differentielles a controle optimal formulation lagrangienne (II). Novi Sad J. Math. 29(3), 211–220 (1999)MathSciNetzbMATHGoogle Scholar
  14. Quandt, J.: On the Hartman–Grobman theorem for maps. J. Differ. Equ. 64(2), 154–164 (1986)MathSciNetCrossRefGoogle Scholar
  15. Sangeorzan, L., David, N.: Some methods of generating fractals and encoding images. In: Proceedings of the 2nd International Conference on Symmetry and Antisymmetry in Mathematics, Formal Languages and Computer Science, Satellite Conference of 3ECM, Brasov, Romania, Transilvania University Publishing House, pp. 337–342 (2000)Google Scholar
  16. Urban, R., Hoskova-Mayerova, S.: Threat life cycle and its dynamics. Deturope 9(2), 93–109 (2017)Google Scholar
  17. Volterra, V.: Fluctuations in the abundance of a species considered mathematically. Nature 118, 558–560 (1926)CrossRefGoogle Scholar
  18. Wilson, G.: Hilbert’s sixteeen problem. Topology 17(1), 55–73 (1978)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceTransilvania University of BraşovBraşovRomania

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