+2353 Okay so I have these questions
With these answers
Now I don't entirely understand what's happening here.
I do understand part a) (but I included it to save you some calculations)
In part b) it is apparently true that an equilibrium solution is asymptotically stable if $$|\lambda_k|<1 \mbox{ } \forall \mbox{ } k$$
where $$\lambda_k$$ is an eigenvalue of the jacobian matrix. Even though intuitively this does seem to make sense, can someone explain this to me?
Then for part c), they say that the $$(c_1_-,c_1_-)$$ equilibrium solution is asymptotically stable for all $$a>0$$ while in part b) it was stated that both equilibrium solutions for $$a=\frac{1}{2} , b = \frac{1}{2}$$ were not asymptotically stable. Perhaps I'm missing something here, but to me this appears as a contradiction.
Reinout 
+11912 oh reinout , i wish i could help u but the math is like " from another world from me " so i cant help ! but i can give u my very famous " all the bast " lol! so i hope u succed in ur search for help ! 
+33614 When it says for all a>0, it has already specified that a must be less than 1/4, so I think it means in the range 0<a<1/4. I might be wrong about this as, for the (r,s) solution it explicitly gives the range as 0 to 3/16.
I calculated the iterates for starting values of (0, 0) and a few different a values (b = 1/2 in all cases). They look like this:
Where succesive iterates are not converging they are clearly oscillating between two values.
Hope this helps rather than confuses!
(Edited to upload the correct figures!)
+893 Hi Reinout
Are you still interested in this question or have you got it sorted ?
