Generalization of poorly studied Dixon models which describe the chaotic regimes via the two dimensional systems of ordinary differential equations was given. New two-dimensional models with numerical calculations which illustrate the chaotic oscillations was conducted.
динамические системы на плоскости, хаотические режимы, модели Диксона, инварианты, показатели Ляпунова, dynamical systems on the plane, chaotic regimes, Dixon models, invariants, Lyapunov exponents
1. E.N. Lorenz, Journal of Atmospheric Science, 20, 30-141 (1963).
2. Strannye attraktory / Pod red. Ya.G. Sinaya, L.P. Shil'nikova. Mir, Leningrad, 1981. 253 s.
3. D.D. Dixon, F.W. Cummings, P.E. Kaus, Phys. Nonlinear Phenom, 65, 109-116 (1993).
4. F.W. Cummings, D.D. Dixon, P.E. Kaus, Astrophys. J, 386, 215-221 (1992).
5. S.P. Kuznecov, Dinamicheskiy haos. Fizmatlit, Moskva, 2006. 356 s.
6. A.P. Kuznecov, A.V. Savin, L.V. Tyuryukina, Vvedenie v fiziku nelineynyh otobrazheniy. Nauchnaya kniga, Saratov, 2010. 134 s.
7. Li Chunbiao, J.C. Sprott, Physics Letters A, 378, 178-183 (2014).
8. http://sprott.physics.wisc.edu/
9. V.H. Fedotov, N.I. Kol'cov, Vestnik Kazan. tehnol. un-ta, 16, 23, 7-9 (2013).
10. V.H. Fedotov, N.I. Kol'cov, Vestnik Kazan. tehnol. un-ta, 16, 23, 10-12 (2013).
11. M. Molaei, S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Int. J. Bifurc. Chaos, 23, 1350188-1 - 1350188-7 (2013).
12. S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Physics Letters A, 377, 699-702 (2013).
13. http:// demonstrations.wolfram.com/ DixonModel ForMagneticFieldOfA Neutron Star.
14. J.C. Sprott, Elegant Chaos: Algebraically Simple Chaotic Flows. World Scientific, Singapore, 2010. 285 p.
15. J. Alvarez-Ramirez, J. Delgado-Fernandez, G. Espinosa-Paredes, Int. J. Bifurcat. Chaos Appl. Sci. Eng. 15, 3023-3029 (2005).
16. A.A. Andronov, E.A. Leontovich, I.I. Gordon, A.G. Mayer, Kachestvennaya teoriya dinamicheskih sistem vtorogo poryadka, Nauka, Moskva, 1966. 568 s.
17. A.A. Andronov, E.A. Leontovich, I.I. Gordon, A.G. Mayer, Teoriya bifurkaciy dinamicheskih sistem na ploskosti, Nauka, Moskva, 1967. 384 s.
18. F. Hartman, Obyknovennye differencial'nye uravneniya, Mir, Moskva, 1970. 400 s.
19. A. Puankare, O krivyh, opredelyaemyh differencial'nymi uravneniyami, Gostehizdat, Moskva-Leningrad, 1947. 385 c.
