SpruceBudworm Spruce bud worm model equations

SpruceBudworm.ar( reset=0, rate=0.1, k1= 20, k2= 1.5, alpha = 0.1, beta = 10.1, mu=0.3, rho=10.1, initx=0.9,inity=0.1,mul, add)

One of a number found in A Brief History of Oscillators and Hair Styles of European Men AASU Math/CS Colloquium, April 2002. 

Euler ODE solver implementation of a model of foliage and budworm density in Canadian forests ( a logistic model + predation).  

x' = k1 x (1-x) - mu*y

y' =  k2 *y * (1 - (y/alpha*x)) - (rho * (y**2/(beta**2 * x**2 + y**2)))

All inputs can have .kr rate UGens plugged in.

Nonlinear oscillators can blow up, treat with caution.

reset- If > 0.0, restart with new initial conditions sampled from initx, inity

rate- update rate for a sample step

k1- equation constant

k2- equation constant

alpha- equation constant

beta- equation constant

mu- equation constant

rho- equation constant

initx- reset value for x

inity- reset value for y

//listen to x and y output with defaults

{Out.ar(0,0.5*SpruceBudworm.ar(0.0))}.play

//be careful with rate range, can blow-up easily here, or just not sound

{Out.ar(0,0.5*SpruceBudworm.ar(0.0,MouseX.kr(0.09,0.1)))}.play

{Out.ar(0,0.5*SpruceBudworm.ar(0.0,,MouseX.kr(0.09,0.1),MouseY.kr(25.0,28.0)))}.play

{Out.ar(0,0.5*SpruceBudworm.ar(Impulse.kr(MouseY.kr(1,50,'exponential')),0.1))}.play

{Out.ar(0,Pan2.ar(0.5*(SpruceBudworm.ar(Impulse.kr(MouseX.kr(1,50)),0.1,24.8,0.5,initx:MouseY.kr(0.2,1.2))[0])))}.play

{10.0*(SpruceBudworm.ar(Impulse.kr(Line.kr(1,200,0.1)),0.1,19.8,0.5,initx:0.6)[0]-1.0)}.plot(0.1)

{10.0*(SpruceBudworm.ar(Impulse.kr(MouseX.kr(1,200)),0.1,19.8,0.5,initx:0.6)[0]-1.0)}.play

{10.0*(SpruceBudworm.ar(Impulse.kr(MouseX.kr(1,200)),0.1,MouseY.kr(19,28),0.5,initx:0.6)[0]-1.0)}.play