For citation:
Bystrai G. P., Studenok S. I. Two-dimensional mappings for nonlinear rotator with a piecewise-constant decay factor raised by periodic shocks. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 6, pp. 24-34. DOI: 10.18500/0869-6632-2002-10-6-24-34
Two-dimensional mappings for nonlinear rotator with a piecewise-constant decay factor raised by periodic shocks
The deriving of difference evolutionary equations for a nonlinear rotator with a piecewise-constant decay factor raised by periodic shocks is considered. The type of nonlinearity is set by the first partial catastrophes («crimp» and «assembly»), and the time between shocks is comparable with relaxation time of a rotator. For set mappings the Lyapunov exponents, depending from two and more parameters are found; the bifurcation diagrams are constructed and some reference bifurcation values of control parameters, are spotted at transition to chaos. Obtained mappings including model equations can serve for the analysis of the first and the second type phase transitions with random dynamics of an order parameter.
1. Schuster HG. Deterministic Chaos: An Introduction. Weinheim: Physik-Verlag; 1984. 220 p.
2. Gilmore R. Catastrophe Theory for Scientists and Engineers. Dover Publications; 1993. 666 p.
3. Kolmanovsky VB. Equations with aftereffects and mathematical modeling. Soros Educational Journal. 1996;(4):122 (in Russian).
4. Gershuni GZ. Hydrodynamic instability. Isothermal flows. Soros Educational Journal. 1997;(2):99–106 (in Russian).
5. Mikhailov IG, Soloviev VA, Syrnikov YP. Fundamentals of Molecular Acoustics. Moscow: Nauka; 1964. 514 p. (in Russian).
6. Bystrai GP. Deterministic chaos in nonlinear problems of thermophysics. In: Arzamastsev AA, editor. Materials of the Second All-Russian Scientific Internet Conference “Computer and Mathematical Modeling in Natural and Technical Sciences”, April-May 2001. Vol. 7. Tambov: Tambov University Publishing; 2001. P. 3–9 (in Russian).
7. Bystrai GP, Moiseeva ON. Development of quantitative methods of the theory of first-order phase transitions and critical phenomena in the liquid-vapor system. In: Metastable States and Phase Transitions. No. 3. Ekaterinburg: Publishing House of the Ural Branch of the Russian Academy of Sciences; 1999. P. 151–166 (in Russian).
8. Anishchenko VS, Neiman AB, Moss F, Shimansky-Geier L. Stochastic resonance: noise-enhanced order. Phys. Usp. 1999;42(1):7–36. DOI: 10.1070/PU1999v042n01ABEH000444.
9. Klimontovich YL. What are stochastic filtering and stochastic resonance? Phys. Usp. 1999;42(1):37–44. DOI: 10.1070/PU1999v042n01ABEH000445.
10. Berge P, Pomeau I, Vidal K. Order within Vhaos. Wiley; 1986. 329 p.
11. Feigenbaum MJ. Universal behavior in nonlinear systems. Los Alamos Sci. 1980;1(1):4–27.
12. Bystry GP. On the mechanism of the emergence of chaotic regimes in the dynamics of structures (using the example of a convex beam). In: Collection of Scientific Papers of the XXX Ural Seminar “Heterogeneous Structures”. Miass: Ural Branch of the Russian Academy of Sciences; 2000. P. 85–91 (in Russian).
13. Bystrai GP, Ivanova SI. Mathematical modeling of nonequilibrium phase transitions and chaotic thermodynamics of evaporation and condensation in the liquid-vapor system. In: Arzamastsev AA, editor. Materials of the Second All-Russian Scientific Internet Conference “Computer and Mathematical Modeling in Natural and Technical Sciences”, April-May 2001. Vol. 7. Tambov: Tambov University Publishing; 2001. P. 10–16 (in Russian).
14. Frenkel YI. Kinetic Theory of Liquids. Moscow: Publishing House of the USSR Academy of Sciences; 1945. 424 p. (in Russian)
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