Thread: hopf bifurcation

hey, i have two simple questions - my notes aren't what they should be.


What is the definition of, and how do i test for a hopf bifurcation in system equations.


And

in permutations of 3d vectors, i know (12) corresponds to swapping x1 and x2 but what does (123) or (321) correspond to?


Thankyou.

1) What is wiki for?



2) (123) means x1 becomes x2, x2 becomes x3, x3 becomes x1 and similarly for (321). These algebraic objects are called - quite clearly - "permutations".