Examples needed

Thread View: comp.theory.dynamic-sys

2 messages

[T] Back to Threads [V] Tree View [G] Group Articles

2 total messages Started by Ranjan Drzzzzt! Bagchi Sun, 31 Jan 1993 22:48

#268

Author: Ranjan Drzzzzt! Bagchi
Date: Sun, 31 Jan 1993 22:48

28 lines
1635 bytes

	Hi.  I'm having a hell of a time finding an example of
a chaotic attractor in a 3-species predator-victim system with either
Lotka-Volterra characteristics, or logistic characteristics.

	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.

	help??

	-rj
	
-- 
Ranjan Bagchi					       Ranjan.Bagchi@umich.edu
oo   oooo  o oo   ooo oo oo   oo       o o  oooo ooo o       o        oooooooo

Re: Examples needed

#269

Author: George Broze
Date: Tue, 02 Feb 1993 17:39

28 lines
1913 bytes

In article <1993Jan31.224819.2673@zip.eecs.umich.edu>, bagchi@quip.eecs.umich.edu (Ranjan Drzzzzt!  Bagchi) writes...

>	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

Thread Navigation

This is a paginated view of messages in the thread with full content displayed inline.

Messages are displayed in chronological order, with the original post highlighted in green.

Use pagination controls to navigate through all messages in large threads.

Back to All Threads