|
This article is cited in 4 scientific papers (total in 4 papers)
METHODICAL PAPERS IN NONLINEAR DYNAMICS
The discrete van der Pol oscillator: Finite differences and slow amplitudes
V. V. Zaytcev Samara State Aerospace University
Abstract:
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.
Keywords:
Self-oscillatory system, van der Pol’s equation, the discrete time, finite differences, slowly changing amplitudes, the shortened equations, the discrete mapping of Thomson selfoscillators.
Received: 04.08.2017
Citation:
V. V. Zaytcev, “The discrete van der Pol oscillator: Finite differences and slow amplitudes”, Izvestiya VUZ. Applied Nonlinear Dynamics, 25:6 (2017), 70–78
Linking options:
https://www.mathnet.ru/eng/ivp47 https://www.mathnet.ru/eng/ivp/v25/i6/p70
|
Statistics & downloads: |
Abstract page: | 296 | Full-text PDF : | 263 |
|