Solutions

Here is demonstrated the effect of changing the growht factor ε.

In[1]:=

Out[6]=

You can find a steady state solution by setting the right hand side of the equations to zero at time t=0:
    
This can be solved for (0) and (0) to obtain the stability conditions
    (0)= and (0)=
Below is an example of a steady solution. A variation of the parameters leads to oscillatory behaviour. The function Unset can be used to clear variables which have super- or subscripts (regular Clear doesn't work).

In[21]:=

Out[25]=

Again the stable situation can be analytically discovered to be
    (0)=, and (0)=.
A stable solution could be obtained if one of the above would be zero, but that's not so interesting. Note also that for some values of the parameters stable situations are impossible (the initial sizes of the populations would have to assume negative values).

In[28]:=

Out[32]=

Created by Mathematica  (April 10, 2007)