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van der Pol oscillator phase plot, with μ varying from 0.1 to 3.0. The green lines are the x-nullclines. The same oscillator phase plot, but with Liénard transform. The Van der Pol Oscillator simulated with the Brain Dynamics Toolbox [1] Evolution of the limit cycle in the phase plane.
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You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
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).
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 ...
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: ...
A plot of position and momentum variables as a function of time is sometimes called a phase plot or a phase diagram. However the latter expression, " phase diagram ", is more usually reserved in the physical sciences for a diagram showing the various regions of stability of the thermodynamic phases of a chemical system, which consists of ...
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 ...