WeaklyNonlinear:

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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 |

//Can be very noisy, high pitched and aliases badly- ie great fun, but watch out for your ears, filter, try out odd param settings. I've turned all the amplitudes down in the following //defaults, high pitched! WARNING {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(SinOsc.ar(MouseX.kr(100,400),0,0.1)),0.0))}.play {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(SinOsc.ar(MouseX.kr(50,1000,'exponential'),0,0.1),0,1,1,MouseY.kr(50,1000,'exponential')),0.0))}.play //with reset {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(SinOsc.ar(MouseX.kr(50,1000,'exponential'),0,0.1),Impulse.kr(3),1,1,MouseY.kr(50,1000,'exponential'), LFNoise0.kr(1,0.4,0.5),LFNoise0.kr(1,10.4,10.5)),0.0))}.play //MouseY controls input strength of forcing oscillator {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(Saw.ar(261.626,MouseY.kr(0.0001,1,'exponential')), freq:MouseX.kr(100,400)),0.0))}.play //2 per second ( {Out.ar(0,Pan2.ar( CombN.ar( Resonz.ar(WeaklyNonlinear.ar(Saw.ar(MouseX.kr(50,2000,'exponential'),0.5),0,1,1,MouseY.kr(100,4000,'exponential')),1000,0.1), 0.05,0.05,1 ) ,0.0))}.play ) //with non zero nonlinear term, van der Pol equation, acts to damp, so a rest is needed to hear many sounds {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(SinOsc.ar(MouseX.kr(10,2000),0,0.1),Impulse.kr(MouseY.kr(0,100)),1,1,440,0,0,-0.01,2,-1,1),0.0))}.play //Duffing equation {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(SinOsc.ar(MouseX.kr(1,1000,'exponential'),0,0.1),0,1,1,MouseY.kr(1,1000,'exponential'),0,0,-0.001,3,0,0),0.0))}.play //make one up... will last for a while then be lost- needs a Trigger control in reset, very aliased {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(SinOsc.ar(MouseX.kr(1,100,'exponential'),0,0.1),Impulse.kr(0.5),1,1,MouseY.kr(1,1000,'exponential'),LFNoise0.kr(10,0.0),LFNoise0.kr(10,0.0),0.005,3,1,0.5),0.0))}.play //highly aliased {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(SinOsc.ar(0,0,0.1),0,1,1,MouseX.kr(110,880,'exponential'),0,0,MouseY.kr(0,1.0)),0.0))}.play //anything happening? {Out.ar(0,Pan2.ar(0.1*WeaklyNonlinear.ar(SinOsc.ar(0,0,0.1),Impulse.kr(10),1,1,MouseX.kr(110,880,'exponential'),0,0,0.5,1,1,MouseY.kr(0,1.0)),0.0))}.play

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

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