For citation:
Tulebaev S. D., Harrasov M. H. Periodic solutions of Gurel - Rossler model. Izvestiya VUZ. Applied Nonlinear Dynamics, 1995, vol. 3, iss. 1, pp. 3-10. DOI: 10.18500/0869-6632-1995-3-1-3-10
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 0)
Language:
Russian
Article type:
Article
UDC:
519.6
Periodic solutions of Gurel - Rossler model
Autors:
Tulebaev Salavat Dilmuhametovich, Bashkir State University
Harrasov Muhammed Hadisovich, Bashkir State University
Abstract:
On the basis of the Bogoljubov’s asymptotic methods the existence of selfoscillating modes and a sequence of the period doubling bifurcation in dynamical Gurel - Rossler model are demonstrated. Qualitative results are confirmed by numerical calculations.
Key words:
Acknowledgments:
In conclusion, the authors express gratitude to V.V. Alekseev for his assistance help.
Reference:
- Gaponov-Grekhov АV, Rabinovich MI. Nonlinear physics. Stochasticity and structures. In: Physics of the XX Century. Development and Prospects. М.: Nauka; 1984. P. 219-280.
- Anishchenko VS. Complex Oscillations in Simple Systems. М.: Nauka; 1990. 312 p. (in Russian).
- Svirezhev YuМ. Nonlinear Waves. Dissipative Structures and Disasters in Ecology. М.: Nauka; 1987. 365 p.
- Alekseev VV, Kornilovsky AN. Ecosystem stochasticity model. Ecol. Model. 1985;28(3):217-229. DOI: 10.1016/0304-3800(85)90084-5.
- Feigenbaum M. J. Universal behavior in nonlinear systems. Los Alamos Science. 1980;1(1):4-27.
- Bogolyubov NN, Mitropolskii YuА. Asymptotic Methods in the Theory of Nonlinear Oscillations. M.: Nauka; 1974. 503 p.
- Gurel D, Gurel O. Oscillations in Chemical Reactions. Berlin: Springer; 1983. 131 p.
- Alekseev VV, Kharrasov MK. On the sequence of period doubling bifurcations in Rossler models. Theor. Math. Phys. 1991;88:741-746. DOI: 10.1007/BF01016342.
Received:
18.05.1994
Accepted:
02.02.1995
Published:
15.09.1995
Journal issue:
- 1525 reads