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.
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References
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)
Bârzu, A., Bourceanu, G., Onel, L.: Nonlinear dynamics. MatrixRom, Bucharest (2003)
Broer, H., Takens, F.: Dynamical Systems and Chaos. Springer, Berlin (2009)
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)
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)
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)
Florea, O., Purcaru, M.: Mathematical modeling and the stability study of some chemical phenomena. Proc. AFASES 1, 525–529 (2012)
Kuznetsov, N.V.: Stability and Oscillations of Dynamical Systems: Theory and Applications. Jyvaskyla Studies of Computing (2008)
Li, J.: Hilbert’s 16th problem and bifurcations of planar polynomial vector fields. Int. J. Bifurc. Chaos 13(1), 47–106 (2003)
Lotka, A.J.: Undamped oscillations derived from the law of mass action. J. Am. Chem. Soc. 42, 1595–1599 (1920)
Lungu, N., Chisalita, A.: Dynamical Systems And Chaos. MatrixRom, Bucharest (2007)
Lupu, M., Postelnicu, A., Deaconu, A.: A Study on the flutter stability of dynamic aeroelastic systems. In: Proceedings CDM , pp. 37–46. Brasov (2001)
Obadeanu, V., Neamtu, M.: Systemes dynamiques differentielles a controle optimal formulation lagrangienne (II). Novi Sad J. Math. 29(3), 211–220 (1999)
Quandt, J.: On the Hartman–Grobman theorem for maps. J. Differ. Equ. 64(2), 154–164 (1986)
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)
Urban, R., Hoskova-Mayerova, S.: Threat life cycle and its dynamics. Deturope 9(2), 93–109 (2017)
Volterra, V.: Fluctuations in the abundance of a species considered mathematically. Nature 118, 558–560 (1926)
Wilson, G.: Hilbert’s sixteeen problem. Topology 17(1), 55–73 (1978)
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Florea, O.A. (2019). Mathematical Modeling of Some Physical Phenomena Through Dynamical Systems. In: Flaut, C., Hošková-Mayerová, Š., Flaut, D. (eds) Models and Theories in Social Systems. Studies in Systems, Decision and Control, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-00084-4_4
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