For citation:
Kuznetsov A. P., Kuznetsov S. P. Nonlinear oscillations, catastrophes, bifurcations, chaos. Educational programs.. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 4, pp. 19-28. DOI: 10.18500/0869-6632-1997-5-4-19-28
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:
Other
UDC:
53:372.8; 537.86
Nonlinear oscillations, catastrophes, bifurcations, chaos. Educational programs.
Autors:
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract:
The scientific programs on the courses "Nonlinear Oscillations", "Catastrophes and Bifurcations", "Dynamic Chaos" are presented. The educational programs, combining each other, form a single complex, focused on early obstacles to cognitive thinking.
Key words:
Acknowledgments:
When developing the courses “Nonlinear Oscillations”, “Catastrophes and Bifurcations”, “Dynamic Chaos”, the results of scientific research supported by grants of the Russian Foundation for Basic Research №. 97-02-16414 and № 96-15-96921 were used.
Reference:
- Mandelshtam LI. Lectures on Oscillation Theory. M.: Nauka; 1972. 417 p. (in Russian).
- Andronov AA, Vitt AA, Khaikin SE. Theory of Oscillators. Oxford: Pergamon Press, 1966. 837 p.
- Rabinovich MI, Trubetskov DI. Introduction to the Theory of Oscillations and Waves. М.: Nauka; 1992. 454 p. (in Russian).
- Anishchenko VS. Complex Oscillations in Simple Systems. М.: Nauka; 1990. 312 p. (in Russian).
- Butenin NV, Neimark YuI, Fufaev NА. Introduction to the Theory of Nonlinear Oscillations. М.: Nauka; 1987. 384 p.
- Haken H. Synergetics. Berlin: Springer; 1978. 358 p. DOI: 10.1007/978-3-642-96469-5.
- Poston T, Stewart I. Catastrophe Theory and Its Applications. N.Y.: Dover Publ.; 1996. 491 p.
- Gilmore R. Catastrophe Theory for Scientists and Engineers. N.Y.: Wiley; 1981. 686 p.
- Arnold VI. Catastrophe Theory. Berlin: Springer; 1992. 150 p. DOI: 10.1007/978-3-642-58124-3.
- Arnold VI, Vaarchenko AN, Gusein-Zade SM. Features of Differentiable Mappings. M.: Nauka; 1982. 304 p.
- Thompson JMT. Instabilities and Catastrophes in Science and Engineering. N.Y.: Wiley; 1982. 226 p.
- Crawford JD. Intoduction to bifurcation theory. Rev. Mod. Phys. 1991;63(4):991-1037. DOI: 10.1103/RevModPhys.63.991.
- Berge Р, Pomeau Y, Vidal CH. Order Within Chaos. N.Y.: Wiley; 1986. 329 p.
- Neimark YuI, Landa PS. Stochastic and Chaotic Osciliations. Dordrecht: Springer; 1992. 500 p. DOI: 10.1007/978-94-011-2596-3.
- Schuster HG. Deterministic Chaos. An Introduction. Weinheim: Physik—Verlag; 1984. 220 p.
- Оtt Е. Chaos in Dynamical Systems. Cambridge: Cambridge University Press; 1993. 385 p.
- Thompson JMT, Stewart HB. Nonlinear Dynamics and Chaos. N.Y.: Wiley; 1986. 376 p.
Received:
13.05.1997
Accepted:
20.08.1997
Published:
17.10.1997
Journal issue:
- 277 reads