For citation:
Zaitsev V. V. The discrete van der paul oscillator: finite differences and slow amplitudes. Izvestiya VUZ. Applied Nonlinear Dynamics, 2017, vol. 25, iss. 6, pp. 70-78. DOI: 10.18500/0869-6632-2017-25-6-70-78
The discrete van der paul oscillator: finite differences and slow amplitudes
For sampling of time in a differential equation of movement of van der Pol oscillator (generator) it is offered to use a combination of the numerical method of finite differences and the asymptotic method of the slowl-changing amplitudes. The difference approximations of temporal derivatives are selected so that, first, to save conservatism and natural frequency of the linear circuit of self-oscillatory system in the discrete time. Secondly, coincidence of the difference shortened equation for the complex amplitude of self-oscillations in the discrete time with Euler’s approximation of the shortened equation for amplitude of self-oscillations in analog system prototype is required. It is shown that realization of such approach allows to create discrete mapping of the van der Pol oscillator and a number of mappings of Thomson type oscillators. The adequacy of discrete models to analog prototypes is confirmed with also numerical experiment.
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