WeaklyNonlinear:

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| UGens > Generators > Chaotic

Extension

Weakly Nonlinear Oscillator

Source: SLUGens.sc

//SLUGens released under the GNU GPL as extensions for SuperCollider 3, by Nick Collins, http://composerprogrammer.com/index.html

Naive Euler ODE solver implementation of the Weakly Nonlinear Oscillator with external perturbation (see Strogatz, Steven H. (1994) Nonlinear Dynamics and Chaos. Addison-Wesley, Reading, MA. pp215 or Pikovsky, Arkady., Rosenblum, Michael., and Kurths, Jurgen. (2001). Synchronization. CUP: Cambridge. pp 189).

D2x +w0*w0*x = alpha*(x^xexponent*+beta)*y^yexponent + input

y= Dx

The nonlinear term is not calculated if alpha is zero. Otherwise it is generated at additional CPU cost.

All inputs can have .kr rate UGens plugged in.

NOTE: Due to an error of implementation this oscillator has an additional distortion component in it- which adds to the sound! WeaklyNonlinear2 is an implementation with this fixed, but this older version is retained for backwards compatibility and because it has an interesting roughness.

input |
audio rate input, acts as external force |

reset |
restart |

ratex |
update rate for x |

ratey |
update rate for y |

freq |
The equation constant w0 (linear oscillator's frequency when alone * 2pi) |

initx |
reset value for u |

inity |
reset value for w |

helpfile source: /usr/local/share/SuperCollider/Extensions/SC3plugins/SLUGens/HelpSource/Classes/WeaklyNonlinear.schelp

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