Geodesic
Van der Pol and Rayleigh oscillators in discrete time
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 7 (2014), pp. 104-114

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New discrete displays of classical self-oscillatory systems — Van der Paul and Rayleigh's oscillators are offered. Displays with the kept temporary characteristics of response of linear system on external influence are received on the basis of combination of methods of parametrical synthesis and invariancy of pulse characteristics of dynamic systems. Examples of generation of regular and chaotic self-oscillations in discrete time are given. For the analysis of self-oscillations in the received discrete systems the method of slowly changing amplitudes is used. The effect of substitution of frequencies in a range of self-oscillations with use of the improved first approach is considered.
Keywords: nonlinear dynamics, discrete time, self-oscillatory system, discrete mapping, high-Q oscillators, method of invariance of impulse responces, effect of substitution of frequencies, dynamic chaos. 
@article{VSGU_2014_7_a9,
     author = {V. V. Zaitsev and S. V. Lindt and A. N. Shilin},
     title = {Van der {Pol} and {Rayleigh} oscillators in discrete time},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {104--114},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_7_a9/}
}
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V. V. Zaitsev; S. V. Lindt; A. N. Shilin. Van der Pol and Rayleigh oscillators in discrete time. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 7 (2014), pp. 104-114. http://geodesic.mathdoc.fr/item/VSGU_2014_7_a9/