For citation:
Kuznetsov A. P. Via computer screen into the world of nonlinear dynamics. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 5, pp. 89-102.
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Russian
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Article
UDC:
621.373
Via computer screen into the world of nonlinear dynamics
Autors:
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract:
A series of computer problems is presented covering the course «Dynamical systems and bifurcations» for students specialized in Nonlinear Dynamics. Examples of computer illustrations are given.
Key words:
Acknowledgments:
The author would like to thank S.P. Kuznetsov, L.V. Krasichkov, and H.C. Bogdanov for their help and useful discussion, as well as all the students who participated in setting up the computer seminars.
The work was supported by the grant of the Federal Target Program “Integration” (№ 696.03). The results of scientific research supported by the RFBR grants № 96-15-96921 were used in staging the classes.
Reference:
- Postnov DE. Bifurcations of regular attractors. Saratov: College; 1996. 102 p.
- Kuznetsov AP, Kuznetsov SP. Nonlinear oscillations, catastrophes, bifurcations, xaoc: training programs. Izvestiya VUZ. Applied Nonlinear Dinamics. 1997;5(4):19-28. (in Russian).
- Trubetskov DI, Rabinovich MN. Introduction to the Theory of Oscillations and Waves. М.: Nauka; 1984. 432 p.
- Nikolis G, Prigozhin I. Cognition of the Complex. M: Mir; 1990. 344 p.
- Moon FC. Chaotic Vibrations: An Introduction for Applied Scientists and Engineers. New York: Wiley; 1987. 309 p.
- Schuster G. Deterministic Chaos: An Introduction. Weinheim: Wiley;1998. 270 p.
- Lichtenberg АJ, Lieberman MA. Regular and Stochastic Motion. N.Y.: Springer; 1983. 499 p. DOI: 10.1007/978-1-4757-4257-2.
- Gibbs HM. Optical Bistability: Controlling Light with Light. Cambridge: Academic Press; 1985. 471 p. DOI: 10.1016/B978-0-12-281940-7.X5001-X.
- Svirzhev YuM. Nonlinear Waves, Dissipative Structures and Catastrophes in Ecology. М.: Nauka; 1987. 368 p.
- Carcasses J, Mira С, Bosch M, Simo C, Tatjer JC. Crossroad агеа — spring area transition(I) Parameter plane representation. Int. J. Bifurc. Chaos. 1991;1(1):183-196. DOI: 10.1142/S0218127491000117.
- Kuznetsov AP, Kuznetsov SP, Sataev IR. Critical dynamics of one-dimensional mappings. Part 2. Two-parameter transition to chaos. Izvestiya VUZ. Applied Nonlinear Dinamics. 1993;1(3-4):17-35. (in Russian).
- Chang SJ, Wortis M, Wright JA. Iterative properties оf а one—dimensional quartic map. Critical lines and tricritical behavior. Phys. Rev. A. 1981;24(5):2669.
- Anishchenko VS. Complex Oscillations in Simple Systems. М.: Nauka; 1990. 312 p. (in Russian).
- Kuznetsov SP, Sataev IR. New types of critical dynamics for two-dimensional maps. Phys. Lett. A. 1992;162(3):236–242. DOI: 10.1016/0375-9601(92)90440-w.
- Berge P, Pomeau Y, Vidal C. Order Within Chaos. Towards a Deterministic Approach to Turbulence. N.Y.: Wiley; 1987. 329 p.
- Proceedings of the Institute of Electrical and Electronics Engineers. 1987;75(8):184.
- Kipchatov AA, Podin SV. Application of the adaptive filtering technique to determine the period of fluctuations of the flow system. Izvestiya VUZ. Applied Nonlinear Dinamics. 1997;5(2-3):72-79. (in Russian).
Received:
03.06.1998
Accepted:
30.10.1998
Published:
25.02.1999
Journal issue:
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