@ JacquesC - Thank you for your hint. However, when I tried PDEtools[dchange] and substituted t by a dummy variable x as specified above, Maple gave an error message "system is singular in right endpoint". @ Robert Israel - First of all, of course you are right with the correct stable value of k(t). Furthermore, in fact I have not taken into account that the set of points leading to the saddle point is two-dimensional (so probably there's another condition I have not yet considered admitting only one path). Your solution methods are quite convincing (although for me no 2 is somewhat harder to understand :). I guess the maple part of the problem is now pretty much easier, thank you a lot.