🚀 go-pugleaf

>>	I do have (from Hastings and Powell, 1991) an example of
>>a chaotic attractor in a system type-II functional response:
>> 
>>dx/dt = x(1-x) - f1(x)y
>>dy/dt = f1(x)y - f2(y)z - d1y
>>dz/dt = f2(y)z - d2z
>> 
>>fn(u) = a_n u/(1 - b_n u)
>> 
>>with constants -- d = ( 0.4 0.01)
>>		  a = (5 0.1)
>>		  b = (3 2.0)
>> 
>>I don't see why I'm having a problem pushing this into
>>a logistic or simple lotka-volterra model, but I'm either
>>getting populations that crash or exponential.
>> 
>>Ranjan Bagchi					       Ranjan.Bagchi@umich.edu
> 
>I tried integrating this with a double-precision, 4th-order Runge-Kutta
>solver using the given parameter values and found a little limit cycle
>in the neighborhood (.3557 < x < .368), (-14.478 < y < -14.446), 
>(-.0054 < z < +.0055).  This result assumes, of course, that I copied
>down all the functions and parameters correctly.
> 
>George

My apologies.  I miscopied the functions.  I tried again and found 6
critical points, two stable [(1,0,0) and (1/6,1/12,95/9)] and four
unstable [(0,0,0), (2/31,145/961,0), (7/6,1/12,-205/9) and (0,1/12,-10/3)].
Of these, I checked only (0,0,0) and (1,0,0) by hand, and tested the
other four numerically.  The last one (0,1/12,-10/3) blew up with regularity
(for what reason I have not yet figured out), but the others headed
to some stable fixed point (as I recall).

George