Relaxation Oscillations
By J. Grasman. Encyclopedia of Complexity and Systems Science, 2009
492 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/43e651e9535ff90b84c75526c49374323a449614
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Citations in the corpus
- Nonlinear control systems - A brief overview of historical and recent advances (2017, background): “[19] 1920s Van der Pol Study of limit cycles in relation with oscillator dynamics [20] 1930s Bode Asymptotic representation of the frequency response [21] 1930s Krylov and Bogoliubov - Existence of invariant measures theorem [22] - Describing function method 1932 Nyquist Regeneration (or Feedback) t”
- Hidden oscillations in dynamical systems (2011, background): “Consider an oscillations arising in the electrical circuit — the van der Pol oscillator [5] ẍ+ μ(x(2) − 1)ẋ+ x = 0 (1) and carry out its simulation for the parameter μ = 2 (see Fig.”
- Piecewise linear differential systems with only centers can create limit cycles? (2017, background): “The existence of limit cycles became important in the applications to the real world, because many phenomena are related with their existence, see for instance the Van der Pol oscillator [29,30], or the Belousov– Zhabotinskii reaction which is a classical reaction of non-equilibrium thermodynamics a”
- Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation (2009, methodology): “The methodologies employed in the previous sections can be utilized to generate a variable order version of the van der Pol equation [41].”
- Mixed-Mode Oscillations with Multiple Time Scales (2012, background): “One of the simplest systems in which the concepts are manifest, and historically perhaps also the first, is the Van der Pol equation [225, 226, 227] with constant forcing λ ∈ R given by”
- Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations (2013, background): “1 Stochastic van der Pol oscillator The van der Pol oscillator was proposed to describe stable oscillation; see van der Pol [52].”