please have a look at the attached picture ...and help me understand what to do next...

thank you for whatever help anyone can provide ...

plz note , i know how to linearize at the equillibrium point which is ( x= m/n , y =a/b )

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- Jan 10th 2009, 01:58 AMcrbnumerical analysis of competing species??
please have a look at the attached picture ...and help me understand what to do next...

thank you for whatever help anyone can provide ...

plz note , i know how to linearize at the equillibrium point which is ( x= m/n , y =a/b ) - Jan 10th 2009, 06:34 AMHallsofIvy
you can change to the "scaled variables" Y= y/(a/b) and X= x/(m/n) by solving those for x and y: x= (m/n)X and y= (a/b)Y. Then the differential equations become

or

and

or

which have equilibrium points at (0, 0) and (1, 1).

You then get

which can be separated as

Integrate that to get g(Y)= f(X).