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MathGroup Archive 2000

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insect population dynamics

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24590] insect population dynamics
  • From: Mark Hunter <mhunter at ecology.uga.edu>
  • Date: Tue, 25 Jul 2000 00:56:21 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I'm trying to use mathematica to run insect population models.  I'm new
to the system, and wolfram support suggested that I post my question
here.

The models are simple predator-prey models.  They are non-linear
simultaneous difference equations.  I've tried using RSolve, but it
doesn't seem to handle the non-linearity.  Is there a way of using a
Do-Loop for the same kind of thing?  A simple example of the model that
I tried is:

RSolve[{a[n + 1] == a[n]*Exp[0.63((1 - a[n]/50)) - 0.068b[n]],  
      b[n + 1] = a[n]*(1 - Exp[-0.068*b[n]]), a[0] == 25,  
      b[0] == 10}, {a[n], b[n]}, n]

I want an output for variables a and n at time n, n+1, etc.

I'd be most grateful for any advice that you can offer, and please don't
underestimate my current level of ignorance.

Many thanks,

Mark Hunter


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