Abstract
Consider a class of autonomous continuous-time dynamical systems whose state at any time can be unambiguously given by a variable x and its derivative \(y =\mathrm{ d}x/\mathrm{d}t\). The phase space of such a system is the phase plane (x, y). Thus, the phase space dimension is N = 2 and the number of degrees of freedom is \(N/2 = 1\).
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- 1.
Andronov et al. [2].
- 2.
These terms were somewhat different in the original definition, although now they are often used synonymously.
- 3.
We will not consider the methods for introducing the norm, in order to avoid excessive mathematics.
References
Andronov, A.A., Vitt, E.A., Khaikin, S.E.: Theory of Oscillations. Pergamon Press, Oxford (1966)
Andronov, A.A., Vitt, A.A., Khaikin, S.E.: Theory of Oscillations, p. 222. Nauka Publisher, Moscow (1981) (in Russian)
Marsden, L.E., McCraken, V.: The Hopf Bifurcation and Its Applications. Springer, New York (1976)
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Anishchenko, V.S., Vadivasova, T.E., Strelkova, G.I. (2014). Dynamical Systems with One Degree of Freedom. In: Deterministic Nonlinear Systems. Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-319-06871-8_4
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DOI: https://doi.org/10.1007/978-3-319-06871-8_4
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