REFERENCES
Berge, P., Pomeau, Y., and Vidal, C., Order Within Chaos. Towards a Deterministic Approach to Turbulence, New York: Wiley, 1986. Translated under the title Poryadok v khaose. O deterministskom podkhode k turbulentosti, Moscow, 2000.
Loskutov, A.Yu. and Mikhailov, A.S., Vvedenie v sinergetiku (Introduction to Synergetics), Moscow, 1990.
Schuster, H.-G., Deterministic Chaos. An Introduction, Weinheim: VCH, 1988. Translated under the title Determinirovannyi khaos: vvedenie, Moscow, 1989.
Chen, G. and Dong, X., From Chaos to Order, World Scientific, 1998.
Sharkovskii, A.N., Ukr. Mat. Zh., 1964, no. 1, pp. 61-71.
Rössler, O.E., Phys. Letters., 1976, vol. 57A, p. 397.
Mackey, M. and Glass, L., Science, 1977, vol. 197, pp. 287-289.
Magnitskii, N.A. and Sidorov, S.V., Differents. Uravn., 2000, vol. 36, no.11, pp. 1488-1492.
Magnitskii, N.A. and Sidorov, S.V., Primenenie instrumentov nelineinoi dinamiki i intellektual'nykh informatsionnykh tekhnologii v ekonomike (Application of Tools of Nonlinear Dynamics and Intelligent Information Technologies to Economics), Moscow, 2002.
Lorenz, E.N., J. Atmos. Sci., 1963, vol. 20, pp. 130-141.
Magnitskii, N.A. and Sidorov, S.V., Differents. Uravn., 2001, vol. 37, no.11, pp. 1494-1506.
Magnitskii, N.A. and Sidorov, S.V., in Nelineinaya dinamika i upravlenie (Nonlinear Dynamics and Control), Emel'yanov, S.V. and Korovin, S.K., Eds., Moscow, 2002, issue 2, pp. 169-184.
Gibbon, J., in Sinergetika (Synergetics), Moscow, 1984, pp. 164-179.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Magnitskii, N.A., Sidorov, S.V. Transition to Chaos in Nonlinear Dynamical Systems Through a Subharmonic Cascade of Bifurcations of Two-Dimensional Tori. Differential Equations 38, 1703–1708 (2002). https://doi.org/10.1023/A:1023851928014
Issue Date:
DOI: https://doi.org/10.1023/A:1023851928014