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The Van der Pol oscillator was originally proposed by the Dutch electrical engineer and physicist Balthasar van der Pol while he was working at Philips. [2] Van der Pol found stable oscillations, [3] which he subsequently called relaxation-oscillations [4] and are now known as a type of limit cycle, in electrical circuits employing vacuum tubes.
Phase portrait of van der Pol's equation, + + =. Simple pendulum, see picture (right). Simple harmonic oscillator where the phase portrait is made up of ellipses centred at the origin, which is a fixed point. Damped harmonic motion, see animation (right).
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English: Chaotic behaviour in the Van der Pol oscillator with sinusoidal forcing. The nonlinear damping parameter is equal to μ = 8.53, while the forcing has amplitude A = 1.2 and angular frequency ω = 2π / 10.
It was named after Richard FitzHugh (1922–2007) [2] who suggested the system in 1961 [3] and Jinichi Nagumo et al. who created the equivalent circuit the following year. [4]In the original papers of FitzHugh, this model was called Bonhoeffer–Van der Pol oscillator (named after Karl-Friedrich Bonhoeffer and Balthasar van der Pol) because it contains the Van der Pol oscillator as a special ...
Van der Pol oscillator; Metadata. This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
Discretized circular Van der Pol system [16] discrete: real: 2: 1: Euler method approximation to 'circular' Van der Pol-like ODE. Discretized Van der Pol system [17] discrete: real: 2: 2: Euler method approximation to Van der Pol ODE. Double rotor map: Duffing map: discrete: real: 2: 2: Holmes chaotic map Duffing equation: continuous: real: 2: ...
Van der Pol was concerned with obtaining approximate solutions for equations of the type ¨ + ˙ + =, where (, ˙,) = ˙ following the previous notation. This system is often called the Van der Pol oscillator. Applying periodic averaging to this nonlinear oscillator provides qualitative knowledge of the phase space without solving the system ...